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IIVIFS-WASPAS: An integrated Multi-Criteria Decision-Making perspective for cloud service provider selection
Future Generation Computer Systems 103 (2020) 91–110
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Future Generation Computer Systems journal homepage: www.elsevier.com/locate/fgcs
IIVIFS-WASPAS: An integrated Multi-Criteria Decision-Making perspective for cloud service provider selection Obulaporam Gireesha a , Nivethitha Somu b , Kannan Krithivasan c , Shankar Sriram V.S. a ,
∗
a
Centre for Information Super Highway (CISH), School of Computing, SASTRA Deemed University, Thanjavur, Tamil Nadu, India Smart Energy Informatics Laboratory (SEIL), Indian Institute of Technology-Bombay, India c Discrete Mathematics Research Laboratory (DMRL), Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu, India b
article
info
Article history: Received 16 March 2019 Received in revised form 20 September 2019 Accepted 27 September 2019 Available online 18 October 2019 Keywords: Cloud service provider selection MCDM QoS attributes Rank centroid Shannon entropy Trustworthy CSPs
a b s t r a c t Cloud service provider selection, an important Multi-Criteria Decision Making (MCDM) problem involves intrinsic relations among the multiple alternatives, attributes and decision experts for the selection of trustworthy Cloud Service Providers (CSPs). Due to uncertain and incomplete nature of the cloud service provider evaluation data, i.e., Quality of Service (QoS) and user feedbacks, the identification of suitable CSPs with accurate service ranking remains an open research challenge. To address the above-mentioned challenge, this work presents an Improved Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregate Sum and Product Assessment (IIVIFS-WASPAS) based cloud service provider selection approach for the identification of Trustworthy CSPs (TCSPs). The proposed CSP selection approach employs integrated objective and subjective weight assessment method and IVIFSWASPAS method to determine the importance of QoS attributes and to rank the TCSPs respectively. Further, a novel preference-attitudinal score and accuracy function of IIVIFS have been designed based on the decision maker’s attitude to rank the TCSPs. Case studies using Cloud Armor, a real-world trust feedback dataset demonstrates the accuracy, effectiveness, and feasibility of IIVIFS-WASPAS approach for CSP selection problem in terms of sensitivity analysis and Rank Reversal Phenomenon (RRP). © 2019 Published by Elsevier B.V.
1. Introduction Over the last few decades, rapid advancements in Information and Communication Technologies (ICT) have an enormous impact on the fifth utility computing - ‘Cloud Computing’ through the provision of data-intensive services and computational resources on a subscription basis [1] . The innate advantages of cloud computing have attracted various governmental, academic and business organizations to migrate their business solutions to cloud infrastructures to make their business processes agile with minimal cost and management effort [2]. However, the proliferation of a wide range of Cloud Service Providers (CSPs) offering functionally-equivalent services with different performance and cost makes the selection of an appropriate and Trustworthy Cloud Service Providers (TCSPs) an unsolved research challenge For example, Google Drive, Onedrive, Bitriz24, MyDrive, etc. provides Storage as a Service (StaaS) at different performance (QoS attributes: availability, response time, price, and so on), cost with varied importance on the QoS attributes (Criteria). Problem Statement and Context: ‘Cloud service provider selection’, a significant and interesting research problem due to the ∗ Corresponding author. E-mail address: [email protected] (Shankar Sriram V.S.). https://doi.org/10.1016/j.future.2019.09.053 0167-739X/© 2019 Published by Elsevier B.V.
existence of a wide range of CSPs (alternatives) and uncertain assessment data (objective and subjective). In general, the performance of the CSPs is well-reflected by the QoS attributes. A user-service QoS evaluation/performance matrix which contains QoS values or users’ feedback values over the QoS attributes forms the major data source for CSP evaluation. Moreover, trustworthiness is a quality metric that expresses the performance of the CSPs with respect to different QoS attributes. Several trustbased service selection approaches based on rough set theory [3– 7], evidence theory [8], probability theory [9,10], fuzzy set theory [11], etc., have been developed for the design of a robust cloud service selection model. CSP selection problem can be formulated as a Multi-Criteria Decision-Making (MCDM) problem due to the intrinsic relationship among the multiple QoS attributes, alternatives and decision makers’ opinions [12–22]. Recent research works based on Fuzzy based MCDM (FMCDM) approaches [23–25] like Intuitionistic Fuzzy Set (IFS) [26–29], Neutrosophic Fuzzy Set (NFS) [30], Hesitant Fuzzy Set (HFS) [31], etc., demonstrated their effectiveness in dealing with uncertain data and ambiguous decisions for cloud service provider selection. However, determining the trustworthiness of the service providers with respect to a set of user-specific QoS attributes is complex due to personal biases in the users’ preferences, imprecise weights of the QoS
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parameters, multi-dimensional evaluation process, vagueness in the decision-making process, and Rank Reversal Phenomenon (RRP) [32]. Solution and Novelty: To address the afore-mentioned issues in CSP selection, this work presents an Improved Interval-Valued Intuitionistic Fuzzy Set-Weighted Aggregate Sum and Product Assessment (IIVIFS-WASPAS) approach for the identification of TCSPs. IIVIFS-WASPAS employs (i) IVIFS — analyse the fuzziness of the user preferences, (ii) Integrated weight assessment method — identify the importance of QoS attributes through IVIFS-Shannon Entropy (SE) for objective weight assessment and Rank-centroid for subjective weight assessment and (iii) IVIFSWASPAS — rank the TCSPs. Further, a novel preference attitudinal score and accuracy function was developed to defuzzify the IVIFS value without loss of information. The major motive behind the application of IVIFS is that it can handle vague and imprecise trust feedback data (crisp data) by expressing satisfaction, dissatisfaction and uncertainty of the CSPs through membership degree/truthfulness, non-membership degree/falsity, and hesitant degree in the form of intervals. Further, WASPAS aggregates Weighted Sum Model (WSM) and Weighted Product Model (WPM) to enable high ranking accuracy in dynamic environment scenarios. In general, the crisp data has uncertainty since it is hard for the users to express their level of satisfaction/dissatisfaction on the cloud service providers with respect to the QoS attributes. Therefore, the conversion of crisp data into IVIFS enables the users to express their satisfaction, dissatisfaction & uncertainty and thereby enabling accurate cloud service ranking. Contributions: The major contributions of the IIVIFS-WASPAS are highlighted as follows: 1. An Improved Interval Valued Intuitionistic Fuzzy Set (IIVIFS) based cloud service provider selection approach is presented to identify the trustworthy CSPs. 2. Uncertainty in the assessment data is handled by converting the user feedbacks (crisp numbers) into IVIFS numbers since it reflects truthfulness, falsity and hesitancy of the CSPs with respect to the QoS attributes. 3. A novel integrated objective and subjective weight assessment approach is designed to determine the importance of the QoS attributes for accurate service ranking. 4. A novel preference attitudinal score and accuracy functions based WASPAS is designed for service ranking without loss of information. 5. The effectiveness of the IIVIFS-WASPAS was demonstrated with the case study using the sample dataset from the Cloud Armor trust feedback dataset in terms of sensitivity analysis and rank reversal phenomenon. The rest of the paper is organized as follows: Section 2 discusses the literature review about cloud service provider selection using different FMCDM approaches. Section 3 provides a detailed insight into the basics of IVIFS, score and accuracy functions of IVIFS. Section 4 presents a novel preference-attitudinal score and accuracy functions for ranking CSPs and working of the IIVIFS, the proposed cloud service provider selection approach. Section 5 presents the case study using Cloud Armor, a trust feedback dataset to analyse the efficiency and reliability of IIVIFS over the state-of-the-art IVIFS based cloud service provider selection approaches. Section 6 concludes the paper. 2. Literature review ‘Cloud service provider selection’ is modelled as a MCDM problem since the trustworthiness of the CSPs can be evaluated
based on: (i) discovering cloud service providers (Alternatives); (ii) identify QoS attributes (Criteria); (iii) assess the ratings of the CSPs’ and weights of the QoS attributes; (iv) aggregate the ratings of the CSPs and weights of the QoS attributes to compute the trustworthiness of each CSP across the QoS attributes, and (v) select the trustworthy CSP. Recent research studies on Fuzzy based MCDM (FMCDM) approaches has gained huge momentum over a wide range of MCDM based CSP selection approaches for the evaluation and identification of trustworthy CSPs [23]. Alam et al. [33] developed Fuzzy Analytic Hierarchy ProcessWASPAS (FAHP-WASPAS), an uncertainty-aware hybrid MCDM approach to evaluate and rank cloud services. FAHP-WASPAS employs FAHP to obtain relative weights of the primary & secondary attributes and WASPAS to rank the cloud services. The efficiency of FAHP-WASPAS was validated using a case study with six realworld public IaaS cloud services (S1, S2, S3, S4, S5, S6), nine main criteria (C1 − C9), and thirty sub-criteria (C 11 − C 13, C 21 − C 23, C 31 − C 33, C 41 − C 44, C 51 − C 53, C 61 − C 63, C 71 − C 74, C 81 − C 83, C 91 − C 94). Further, sensitivity analysis was conducted to verify the robustness of FAHP-WASPAS. Mohamed Abdel-Basset et al. [30] presented a Neutrosophic Multi-Criteria Decision Analysis (NMCDA) technique to estimate the quality of cloud services. The neutrosophic concept has been utilized to aggregate different opinions of the decision makers and improve their consistency rate. Analytic Hierarchy Process (AHP) was introduced in neutrosophic concept to handle ambiguous and inconsistent information presented in the procedure of cloud service estimation. The performance of NMCDA was evaluated using a case study of big e-learning service provider company in Egypt. It considered three cloud service alternatives (Dropbox, Google Drive, and Microsoft Sky Drive) and five criteria (Security, Performance, Accessibility, Scalability, and Adaptability) to select appropriate cloud service provider that provide safety and privacy to the company. Marija Paunovi et al. [34] proposed a two-stage Fuzzy Logic (2sFL) model based on FAHP and fuzzy logic approaches to evaluate cloud service suppliers. The fuzzy logic utilized in 2sFL model minimizes the subjectivity of the decision makers. 2sFL model consists of two stages: (i) The first stage represents the input parameters (estimate the relationship between experts expressed in fuzzy numbers) and output (total evaluation of the cloud suppliers) and (ii) Second stage utilizes the fuzzy logic and approximate reasoning to observe the variables and define them by fuzzy sets. A simulation experiment with three cloud service suppliers (CS1, CS2, CS3), three experts, and five technology perspective terms (criteria-performance, capability, service level, quality & security, and privacy) was carried out using MATLAB to validate the efficiency and rationality of 2sFL model. Aveek Basu and Sanchita Ghosh [35] applied Fuzzy based Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) technique to identify an appropriate cloud service provider and cloud type for an organization. The performance of FTOPSIS was assessed with three different experts (D1, D2, D3) to evaluate three types of cloud service providers (Amazon Web Services, IBM Bluemix, Google Compute Engine) over nine features (Business size support, Support for versatile industries, Control interface features, Availability of support services, Server OD types, Preconfigured operating systems, Available runtimes, Middleware, Native databases). Gülçin Büyüközkan et al. [36] proposed a novel Group Decision Making (GDM) based IVIF MCDM techniques for the Cloud Computing Technology Provider Selection (CCT PS). IVIF MCDM techniques such as Interval-Valued Intuitionistic Fuzzy AHP (IVIF AHP) (determine the weights of criteria and subcriteria), IVIF COmplex PRoportional ASsessment (IVIF COPRAS), IVIF multi-objective optimization by ratio analysis plus the full multiplicative form (IVIF
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MULTIMOORA), and IVIF VišekriterijumskoKompromisnoRangiranje (IVIF VIKOR) rank the CCT providers based on the Decision Makers (DMs) evaluation of alternatives with respect to the criteria. The performance of GDM based IVIF MCDM techniques was evaluated using a case study of ABC Group with three DMs (Vicechancellor, Professor from the academy and IT Manager), six major criteria & 27 sub-criteria and four CCT providers (Amazon Cloud, Google Cloud, IBM Cloud and Azure Cloud) in terms of availability and flexibility. Rakesh Ranjan Kumar et al. [11] designed a novel cloud service selection model based on AHP and Fuzzy TOPSIS to rank cloud service providers. The overall process comprises of three major steps: (i) Identify evaluation criteria to select cloud service providers, (ii) Apply AHP to determine the importance of evaluation criteria, and (iii) Apply Fuzzy TOPSIS to rank cloud services. The efficiency and robustness of the AHP and Fuzzy TOPSIS model was validated using a sample dataset (six cloud database servers over ten criteria) obtained from Cloud Harmony reports and compared with state-of-the-art MCDM approaches like AHP and improved TOPSIS in terms of sensitivity analysis. Neda Tanoumand et al. [37] proposed FAHP technique which employs Fuzzy Extent Analysis (FEA) method to select the suitable cloud service provider for the demanding enterprise. FEA has been used to elicit weights of the criteria with respect to each cloud service provider (alternative) and FAHP choose the optimal cloud service provider for the enterprises. A pilot case study with five cloud service providers (Amazon, Windows, Google, Rackspace, and IBM) and six criteria (acquisition cost and transaction cost, availability, storage capacity, CPU, performance, and security) was used to assess the performance of FAHP technique. Sangwon Lee and Kwang-Kyu Seo [38] proposed a hybrid MCDM model that integrates Balanced Score Card (BSC), Fuzzy Delphi Method (FDM), and Fuzzy Analytical Hierarchy Process (FAHP) to select appropriate IaaS cloud services for organizations. The hybrid MCDM model employs BSC for the identification of the decision-making factors; FDM for the identification of the critical decision-making factors and FAHP to determine the weights of BSC criteria and sub decision-making factors. Further, FAHP was used to rank and select the best cloud service provider. The performance and efficiency of the hybrid MCDM cloud service selection model was evaluated using a case study with four BSC criteria (Financial, Customer, Internal business process, Learning and growth), fourteen decision-making factors and five cloud service providers. Further, the robustness of the proposed model was validated using sensitivity analysis under the consideration of diversified and numerous expert groups. Sun Le et al. [39] proposed a Cloud-Fuzzy User-oriented Cloud SeRvice Selection (Cloud-FuSeR) System to recommend top-K cloud services. The efficiency of Cloud-FuSeR was evaluated using a case study of cloud storage service selection based on two aspects, namely service function matching using Fuzzy LightWeight (FLW) similarity model and ranking cloud services using FTOPSIS method in terms of Mean Squared Error of Ranks (MSER), TOP rank matched count (TOP), Match count (MATCH), and variation between TOP and expected results of the TOPSIS method. Christian Esposito et al. [40] formulated fuzzy logic (express vagueness in the subjective preferences), fuzzy inference, Dempster–Shafer theory of evidence (service provider selection), and game theory (obtain trustworthy service providers by maximizing the user requirements satisfaction and minimizing the storage services price) for cloud storage service provider selection. Simulation on a testbed with 30 storage service providers and 4 QoS attributes was carried out using Objective Modular Network Testbed in C++ (OMNeT++) to validate the efficiency and quality of the presented cloud service selection model. Hua ma et al. [41] proposed Cloud service Interval Neutrosophic Set (CINS) based on Interval Neutrosophic Set (INS) and
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time period features of cloud services to select the trustworthy cloud service providers. INS measure the uncertainty of cloud service providers and compare the candidate service providers with trade-off between performance-costs and potential risks through the cloud model. Further, entropy weight measure was defined to compute the weights of the time periods to compute the difference between the candidate service providers. The experiments were carried out using WS-DREAM #3, a real-world dataset to analyse the performance of CINS in terms of risk-sensitive and performance-cost-sensitive service selection modes. S.P. Wan and J. Xu [42] developed a novel Multi-Attribute Group Decision-Making (MAGDM) with Triangular Intuitionistic Fuzzy Numbers (TIFNs) to evaluate and select the trustworthy services. The TIFNs consider the risk preference of DMs and their weights are determined based on the similarity between the individual and the average decision. The efficiency of MAGDM with TIFNs was validated using a case study of online supplier selection with three DMs, five trust factors (product quality (a1 ), service attitude (a2 ), technology security (a3 ), website design embodies appearance & ease use (a4 ), and shipping speed (a5 )) and three sellers Handuyishe (S1 ), Niman (S1 ) and Liebo (S3 ). Santoso Wibowo et al. [23] presented a fuzzy Multi-Criteria Group Decision Making (MCGDM) method that employs TOPSIS and the Choquet integral operator to evaluate the performance of cloud services in an uncertain environment. The efficiency of fuzzy MCGDM method was validated using a case study of Company A, an e-learning service provider with four cloud service alternatives (iCloud (A1 ), hiCloud (A2 ), Cloud drive (A3 ) and SmartCLOUD (A4 )), three DMs and five criteria (security (C1 ), performance (C2 ), service accessibility and usability (C3 ), scalability (C4 ) and adaptability (C4 )). Jingyi Bo et al. [43] proposed a new Multiple Attribute Decision Making (MADM) method with intuitionistic fuzzy information to assess the performance of cloud computing service evaluation system. The applicability and availability of the proposed model was verified using four alternatives (A1 , A2 , A3 and A4 ) on five attributes (security & risk (C1 ), data (C2 ), services (C3 ), resources (C4 ) and economic dimensions (C5 )). Thiruselvan Subramanian and Nickolas Savarimuthu [24] proposed a CloudSelect framework for cloud service evaluation and selection satisfying consumer’s requirements in cloud marketplace. The CloudSelect includes Fuzzy Analytic Network Process (FANP) to determine the relative weight of criteria and fuzzy TOPSIS, fuzzy Elimination and Choice Translating Reality (ELECTRE) to evaluate and rank the cloud services. The efficiency and robustness of the CloudSelect framework was validated using a case study on multimedia company with six collaboration tool providers (A1 , A2 , A3 , A4 , A5 and A6 ) over six criteria and compared with state-of-the-art MCDM approaches like SMICloud and MCISS in terms of computational complexity and sensitivity analysis. Gai-Li Xu et al. [44] developed a novel MAGDM with IVIFSs for cloud service selection. The decision experts’ preference values are expressed in the form of IVIFSs since it is flexible to measure the qualitative attributes than the crisp numbers. The extended Grey Relational Analysis (GRA) and multi-objective programming model used to determine the weights of decision experts and attributes. Further, the score and accuracy function has been used to rank the cloud services. The efficiency of the presented model was illustrated with an example of four experts (e1 , e2 , e3 and e4 ), four cloud services (SAP Sales on Demand (A1 ), Salesforce Sales Cloud (A2 ), Microsoft Dynamic CRM (A3 ) and Oracle Cloud CRM (A4 )) over five attributes (performance (u1), payment (u2), reputation (u3), scalability (u4 and security (u5)). Wenjuan Fan et al. [45] developed a novel hybrid two-stage model that employs fuzzy gap evaluation model (first stage) and
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an Evidence Reasoning (ER) approach (second stage) for Cloud service Trustworthiness Evaluation (CTE). The first stage identifies the gap between the importance and performance criteria to evaluate the quality of cloud service providers. The second stage based on the belief structure performs robust decision making by analysing CTE from different perspectives. The performance of the hybrid model was analysed using a case study on public storage services and business management services provided by Nirvanix and BMC software in terms of Performance-Importance (P-I), Delivery-Importance (D-I), and Performance-Delivery (P-D) perspectives of cloud service users and cloud service providers. Chen-Tung Chen et al. [46] proposed a decision-making model that integrates fuzzy AHP with Interval-Valued Fuzzy Set (IVFS) to determine the fuzzy weights of criterion. Further, 2-tuple linguistic variables express the performance rating of the cloud service providers (alternatives) and obtain the ranking of cloud service providers. A case study with three cloud computing suppliers (A1 , A2 , A3 ), three decision-makers (p1 , p2 , p3 ) and 9 sub-criteria (C11 , C12 , C13 , C21 , C22 , C23 , C31 , C32 , C33 ) was used to assess the performance of the presented decision-making model. The above-mentioned variants of FMCDM approaches employs different factors and techniques for the identification of TCSPs. However, these methods do not address vagueness and uncertainty in the evaluation data and Rank Reversal Phenomenon (RRP) since they consider only the user’s satisfaction and dissatisfaction with respect to the QoS attributes rather than user uncertainty. Therefore, this research work presents an Improved Interval Valued Intuitionistic Fuzzy Sets (IIVIFSs) based cloud service selection approach which employs IVIFS, integrated weight assessment method, preference attitudinal based score and accuracy function and WASPAS to address the existing challenges in the CSP selection problem. 3. Materials and methods
Interval-Valued Intuitionistic Fuzzy Set (IVIFS) formulated by Atanassov and Gargov is defined in terms of interval numbers rather than crisp numbers to express the Membership Degree Function (MDF) and the Non-Membership Degree Function (NMDF) [47]. Further, the Hesitancy Degree Function (HDF) is defined using MDF and NMDF. Definition 3.1 ([48]). Let ϓ be the universe of discourse and ß is ´ ) in ϓ is defined as in Eq. (1). any element in ϓ, then IFS (υ ß, fυ´ (ß) , ῆυ´ (ß) |ß ∈ ϓ
{⟨
⟩
}
(1)
where, fυ´ (ß) and ῆυ´ (ß) is the MDF and the NMDF of υ´ , respectively. For each point in ß, where ß ∈ϓ, fυ´ (ß) , ῆυ´ (ß) ∈ [0, 1] and 0 ≤ fυ´ (ß) + ῆυ´ (ß) ≤ 1. For each IFS (υ´ ) in ß, let þ (ß) = 1 − fυ´ (ß) − ῆυ´ (ß) be the indeterminacy degree or hesitancy degree (uncertainty degree) function of the element ß to the set υ´ [48,49], where 0 ≤ þ (ß) ≤ 1, ∀ ß ∈ ϓ. For a given element ß, the pair fυ´ (ß) , ῆυ´ (ß) is defined as an Intuitionistic Fuzzy (IFN) [50]. Without the loss of ( Number ) generality, use ζ = fζ , ῆζ to represent IFN that satisfies fζ ∈ [0, 1] , ῆζ ∈ [0, 1] and 0 ≤ fζ + ῆζ ≤ 1.
(
)
Definition 3.2 ([51]). Suppose ϓ is a universe of discourse and ß is any element in ϓ, then IVIFS (Ʋ) in ϓ is defined as in Eq. (2).
Ʋ=
ß, ƑƲ (ß) , ȠƲ (ß) |ß ∈ ϓ
{⟨
⟩
}
þƲ (ß) = 1 − ƑƲ (ß) − ȠƲ (ß) = HƲ (ß)+ , HƲ (ß)−
[
]
] [ = 1 − ΨƲ (ß)− − NƲ (ß)− , 1 − ΨƲ (ß)+ − NƲ (ß)+
(2)
where, ƑƲ (ß) : ϓ → Γ ([0, 1]) and ȠƲ (ß) : ϓ → Γ ([0, 1]); Γ ([0, 1]) represents the set of all closed sub intervals of [0, 1].
(3)
Therefore, the Interval-Valued Intuitionistic Fuzzy Value (IVIFV) or Interval-Valued Intuitionistic Fuzzy Number (IVIFN) ] ([ or IVIFS (Ɽ) can be represented as Ɽ = ΨƲ (ß)+ , ΨƲ (ß)− ,
] ([ − + = ]) ΨƲ (ß) , ΨƲ (ß) , [ or Ɽ ] NƲ (ß)+ , NƲ (ß)− , HƲ (ß)+ , HƲ (ß)− . NƲ (ß)+ , NƲ (ß)−
[
])
[
Definition 3.3 ([51]). If Ẋ, Ẏ ∈ IVIFS (ϓ), then the subset relation is represented as Ẋ ⊂ Ẏ, if and only if ΨẊ (ß)+ ≤ ΨẎ (ß)+ , ΨẊ (ß)− ≤ ΨẎ (ß)− and NẊ (ß)+ ≥ NẎ (ß)+ , NẊ (ß)− ≥ NẎ (ß)− , ∀ ß ∈ ϓ. Definition 3.4 ([51]). The complement (Ɽc ) of IVIFS Ɽ = [ƑƲ (ß), ȠƲ (ß), þƲ (ß)] is defined by (Ɽc ) = [ȠƲ (ß), ƑƲ (ß), þƲ (ß)]. Definition 3.5 ([52]). The Schweizer-Sklar (SS) operations involve SS-Sum, SS-Difference (subtraction), SS-Product, and SS-Division. The SS-Difference and SS-Division are derived based on the additive inverse and multiplicative inverse of SS-Sum and SS-Product (Special cases of Archimedean t-norm and t-conorm (ATT)). − − + − + − and Q = Ƒ+ Let P = Ƒ+ Q , ƑQ , ӃQ , ӃQ P , ƑP , ӃP , ӃP be the two IVIFS, then the relation among MDF, NMDF and SS operational rules (γ < 0) of IVIFS are defined as in Eqs. (4)–(8).
] [
([
])
] [
([
+ − − + + − − P ≤ Q ⇔ Ƒ+ P ≤ ƑQ , ƑP ≤ ƑQ , ӃP ≤ ӃQ , ӃP ≤ ӃQ
3.1. Interval-Valued Intuitionistic Fuzzy Set (IVIFS)
υ´ =
For our convenience, ) and upper el( ) we (represent the lower ements of MDF ƑƲ (ß) as( ΨƲ ()ß)+ ,(ΨƲ (ß)− and lower ) and upper elements of NMDF ȠƲ (ß) as NƲ (ß)+ , NƲ (ß)− , such that 0 ≤ ΨƲ (ß)− + NƲ (ß)− ≤ 1, ΨƲ (ß)+ , NƲ (ß)+ ≥ 0, ∀ ß ∈ ϓ. For each element ß ∈ ϓ, the interval-valued Hesitancy Degree (HD) of Ʋ is defined as in Eq. (3).
([
) + γ
) γ1
) + γ
(4)
]
+ 1 − ƑQ − 1 , , ) γ1 ( )γ − 1 1 − 1 − ƑP + 1 − Ƒ− Q [ ( ) γ1 ]) +γ +γ ӃP + ӃQ − 1 , ( −γ ) γ1 γ ӃP + Ӄ− Q −1 ([ ) ) γ1 ] )γ ( (( + γ − 1 + 1 + Ƒ 1 − 1 − Ƒ+ , P Q P⊖Q= , ( ) ) γ1 (( ) − γ − γ 1 − 1 − ƑP + 1 + ƑQ − 1 [ ( ) γ1 ]) γ +γ Ӄ+ , P − ӃQ − 1 ) γ1 ( −γ γ ӃP − Ӄ− − 1 Q ([ ( ) γ1 ] γ +γ ƑP + Ƒ+ − 1 , Q P⊗Q= , ( −γ ) γ1 −γ ƑP + ƑQ − 1 [ (( )γ ( )γ ) 1 ]) 1 − 1 − Ӄ+ + 1 − Ӄ+ −1 γ , P Q (( )γ ( )γ )1 1 − 1 − Ӄ− + 1 − Ӄ− −1 γ P Q ⎛⎡ ( γ γ ⎤ 1 + +γ ) γ Ƒ+ P ƑQ +1−ƑQ , + ⎜⎢ ⎥ ƑQ P ⊘ Q = ⎝⎣ ( ⎦, 1 −γ −γ −γ ) P⊕Q=
1−
((
1 − ƑP
((
) − γ
ƑP ƑQ +1−ƑQ Ƒ− Q
⎡
(
Ӄ− P
γ
(
1−Ӄ+ P
(
])
(6)
(7)
γ
)γ ( )γ γ + Ӄ− − Ӄ− P −1 P
) γ1
⎢ 1− , ⎢ Ӄ− P ⎢ ⎢ ( ) γ1 ( )γ ( )γ ⎢ γ γ Ӄ− 1−Ӄ+ + Ӄ− −Ӄ− ⎣ Q Q Q −1 Q 1− Ӄ− P
(5)
⎤⎞ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎦⎠
(8)
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
In this work, the SS operational laws are used for cloud service selection due to the presence of variable parameter (γ ; γ < 0) that is superior to the basic IVIFS operations and provides flexibility [53]. To compare two IVIFS and rank the IVIFS, we review the existing score and accuracy functions. Definition 3.6 ([54]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS (0 ≤ Ƒ+ ≤ Ƒ− ≤ 1, 0 ≤ Ӄ+ ≤ Ӄ− ≤ 1, and 0 ≤ Ƒ− + Ӄ− ≤ 1), the score function (S) of an IVIFS (J) can be represented as in Eq. (9).
([
] [
])
Ƒ+ − Ӄ+ + Ƒ− − Ӄ−
(9) , ∀ SXu (J) ∈ [−1, 1] 2 The larger the score value of the IVIFS (SXu (J)), the larger the IVIFS (J). Suppose, if any two IVIFS are equal, then the accuracy function is required to measure the accuracy of MDF and NMDF of IVIFS. SXC (J) =
Definition 3.7 ([54]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS (0 ≤ Ƒ+ ≤ Ƒ− ≤ 1, 0 ≤ Ӄ+ ≤ Ӄ− ≤ 1, and 0 ≤ Ƒ− + Ӄ− ≤ 1), the accuracy function (A) of an IVIFS (J) is defined as in Eq. (10).
] [
([
])
Ƒ+ + Ƒ− + Ӄ+ + Ӄ−
, ∀ AXC (J) ∈ [0, 1] (10) 2 The larger the accuracy value of IVIFS (AXC (J)), the larger the IVIFS (J).
AXC =
Definition 3.8 ([55]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS, a novel accuracy function (N) of an IVIFS (J) is defined as in Eq. (11).
([
+
Ӄ +Ӄ
] [
])
−
, ∀ NYe (J) ∈ [−1, 1] (11) 2 Ye et al. [55] formulated a different expression to measure the accuracy degree of an IVIFS (Eq. (9)). The higher the accuracy value (NYe (J)), the greater the degree of accuracy of IVIFS (J).
NYe (J) = Ƒ+ + Ƒ− − 1 +
Definition 3.9 A ]) novel accuracy function (Ԓ) of an IVIFS, ] ([56]). [ ([ J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− can be computed as in Eq. (12).
ԒLS (J) =
( ) ( ) Ƒ+ + Ƒ− − Ӄ− 1 − Ƒ− − Ӄ+ 1 − Ƒ+ 2
,
∀ ԒLS (J) ∈ [−1, 1]
(12)
The larger the accuracy value of IVIFS (ԒLS (J)), the greater the IVIFS (J).
([ ] [ + − ]) − Definition[ 3.10 ([57]). Let J =[ Ƒ+ , Ƒ , Ӄ ,Ӄ be an IVIFS, ] ] such that Ƒ+ , Ƒ− ⊆ [0, 1] , Ӄ+ , Ӄ− ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the score function (ϑ) of an IVIFS (J) defined by Wang and Chen is given in Eq. (13).
ϑWC (J)
Ƒ+ + Ƒ− +
√ − −( ) √ ( ) Ƒ Ӄ 1 − Ƒ+ − Ӄ+ + Ƒ+ Ӄ+ 1 − Ƒ− − Ӄ−
=
2
∀ ϑWC (J) ∈ [0, 1]
,
(13)
The larger the score value of IVIFS (ϑWC (J)), the higher the IVIFS (J). − + − Definition[ 3.11 ([58]). Let J =[ Ƒ+ , Ƒ be an IVIFS, ] ] , Ӄ ,Ӄ such that Ƒ+ , Ƒ− ⊆ [0, 1] , Ӄ+ , Ӄ− ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the score function (S) of an IVIFS (J) is represented in Eq. (14).
([
SNWC (J) =
] [
])
( + )( ) ( )( ) Ƒ + Ƒ− Ƒ+ + Ӄ+ − Ӄ+ + Ӄ− Ƒ− + Ӄ− 2
,
95
∀ SNWC (J) ∈ [−1, 1]
(14)
The larger the score value of IVIFS(SNWC (J)), the higher the degree of score of the IVIFS (J). − + − Definition[ 3.12 ([58]). Let J =[ Ƒ+ , Ƒ be an IVIFS, ] ] , Ӄ ,Ӄ + − + − such that Ƒ , Ƒ ⊆ ([0,)1] , Ӄ , Ӄ ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the accuracy function Ӑ of an IVIFS (J) is defined as in Eq. (15).
([
ӐNWC (J) ( =
1 − Ƒ+ + Ƒ−
)(
] [
])
1 − Ƒ+ − Ӄ+ + 1 − Ӄ+ + Ӄ−
)
(
)(
1 − Ƒ− − Ӄ−
2
∀ ӐNWC (J) ∈ [0, 1]
) ,
(15)
) ( The larger the accuracy value of IVIFS ӐNWC (J) , the higher the degree of accuracy of the IVIFS (J). + − + − Definition ([ + − ] 3.13 [ + ([54]). ]) If P = ƑP , ƑP , ӃP , ӃP and Q = − ƑQ , ƑQ , ӃQ , ӃQ are two IVIFS, then the following constraints should satisfy the score function (S) and the accuracy function (A) of IVIFS.
([
] [
])
(1) If S (P) > S (Q), then P > Q. (2) If S (P) = S (Q), then consider the conditions listed below:
• If A(P) > A(Q), then P > Q. • If A (P) = A(Q), then P = Q. Where, S (P) and S (Q) represent the score functions of IVIFS. Similarly, A (P) and A(Q) indicates the accuracy functions of IVIFS. Different score and accuracy functions of IVIFS (Eqs. (9)–(15)) provide better ranking of the alternatives. However, there exists inaccuracy in ranking when the sum of lower bound of the membership degrees and the sum of the upper bound of non-membership degrees are equal. Further, Eqs. (9)–(15) does not fully utilize the IVIFS information (MDF, NMDF, and HDF) and therefore leads to imprecise ranking. To address the same, we present a novel preference-attitudinal score and accuracy functions using hesitancy degree for ranking IVIFS (Section 4.1). 4. Improved Interval-Valued Intuitionistic Fuzzy Set: Proposed cloud service provider selection approach 4.1. An improved score and accuracy function of IVIFS based on the preference attitude of assessor/decision maker/user IIVIFS, the proposed cloud service provider selection approach evaluates the cloud service providers based on the aggregated IVIFS. Therefore, it is necessary to find out the ways to compare two IVIFS for accurate service ranking. There exists several score and accuracy functions to compare two IVIFS, however they fail to identify the exact difference between two IVIFS. To address the above-mentioned challenge, we present a novel preference attitudinal based accuracy and score function with an attitudinal parameter in double integral for IVIFN. The proposed accuracy and score function is the extension of Jian Lin et al. work on preference attitudinal accuracy and score functions of IFN [59]. 4.1.1. The preference attitudinal accuracy function Definition 4.1. Let δ = feasible domain of {
U+ , U− , N+ , N− be an IVIFN. The IVIFN (δ) }is defined as FDδ ( + + H+ ; U− ≤X≤U− +H− ) = (X, Ү) NU+ ≤≤ҮX≤≤NU+ + where, H+ = 1 − U− − + +H ; N− ≤Ү≤N− +H−
([
] [
])
N− and H− = 1 − U+ − N+ . By considering the hesitancy degree of δ , the feasible domain (FDδ )indicates the set of feasible interval-valued intuitionistic fuzzy numbers with respect to δ .
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Definition 4.2. Let δ = U+ , U− , N+ , N− , H+ , H− be an IVIFN. The preference attitudinal accuracy function of δ is given in Eq. (16).
([
Aρ (δ) =
∫∫
1 area (FDδ )
] [
] [
])
(ρ X + (1 − ρ) Ү) dXdҮ
(16)
FDδ
Where, FDδ and area (FDδ ) represent the feasible domain of IVIFN and the area of feasible domain (FDδ ) respectively. The parameter ρ (ρ ∈ [0, 1]) indicates the assessor’s (or user’s) preference attitude or the level of decision maker towards the positive, negative, and neutral information, i.e., ρ = 0.5 specifies the assessor or decision maker is neutral to the positive and negative information. average value of accuracy The term Aρ (δ) represents the ∫∫ function over FDδ . The integral part FD (ρ X + (1 − ρ) Y) dXdY δ is equal to the volume of the triangular prism O1 . It means that Aρ (δ) can be considered as an average height of oblique triangular prism O1 . From Definition 4.1, we define the area of feasible domain (FDδ ) (Eq. (17)). 1
)2 1 ( + − )2 1 (( area (FDδ ) = H = H ,H = 1 − U− − N− , 2 2 )2 2
) + 2
+
(
1−U −N
(17)
(ρ X − (1 − ρ) Y) dXdY (∫ ∫ + −
FDδ
,1−N
]
)
1−X
(ρ X − (1 − ρ) Y) dY dX [N+ ,N− ] [U+ ,U− ] )2 1( = 1 − U+ − U− − N+ − N− 6( ) ) ( × U+ + U− − 2 N+ + N− − 1
=
+
ρ(
1 − U+ − U− − N+ − N−
)2
(6 ) × U+ + U− + N+ + N− + 2
(22)
Based on Eqs. (17) and (22), the preference attitudinal score function of IVIFS is defined in Eq. (23). Sρ (δ) =
)
U+ + U− − 2 N+ + N− − 1
ρ( 3
3 +
U + U + N+ + N− + 2
(
Sρ (δ) = ρ
)
X
(ρ X + (1 − ρ) Y) dX dY
=
[U+ ,U− ] [N+ ,N− ] )2 1( 1 − U+ + U− − N+ − N− = 6( ( )) × 1 − U+ + U− + 2 N+ + N−
ρ(
1 − U+ + U− − N+ − N−
2
]
−
)
(23)
Eq. (23) can be rewritten as in Eq. (24).
(ρ X + (1 − ρ) Y) dXdY (∫ ∫ + − [1−N
,1−N
[1−N
+
FDδ
+
∫∫
(
Since,
∫∫
Where, FDδ indicates the feasible domain of IVIFN (δ) and Sρ (δ) is the average score function over FDδ . If the term ϑup indicates the volume of P2 and ϑbelow is the volume of P3 , then ∫∫ (ρ X − (1 − ρ) Ү) dXdҮ = ϑup − ϑbelow . Accordingly, Sρ (δ) FDδ can be considered as the average values of variable T over FDδ . Since,
+ (1 − ρ)
)2 (
U+ − U− − N+ − N−
)
)
2 U+ + U− − N+ − N− + 1 3 ( ) U+ + U− − 2 N+ + N− − 1 3
(24)
In Eqs. (20) and (24), integer 1 (assumption H+ + H− = 1) is replaced with hesitancy degree to utilize full IVIFS information, i.e., MDF, NMDF, and HDF to obtain the ranking without loss of information.
(18) Therefore, the preference attitudinal accuracy function is defined in Eq. (19).
(
Aρ (δ) =
1 − U+ + U− + 2 N+ + N−
)
3 ( ) + ρ U+ + U− − N+ − N−
(19)
Eq. (19) can also be written as in Eq. (20).
)
(
Aρ (δ) = ρ
2 U+ + U− − N+ − N− + 1
+ (1 − ρ)
3 ) ( 2 N+ + N− − U+ − U− + 1
(20)
3
Since the user’s/decision maker’s attitude is dynamic, it is difficult to determine the exact or precise value of parameter (ρ). To address this issue, we consider the preference attitude of user towards the information to estimate the appropriate value of parameter (ρ). Table 1 presents the user’s attitude towards the information with the corresponding value of the parameter (ρ). 4.1.2. The preference attitudinal score function Definition 4.3. Let δ = U+ , U− , N+ , N(− be) an IVIFN. The preference attitudinal score function of δ Sρ (δ) is defined in Eq. (21).
([
Sρ (δ) =
1 area (FDδ )
∫∫ FDδ
] [
])
(ρ X − (1 − ρ) Ү) dXdҮ
(21)
4.2. IIVIFS-WASPAS: Working In this work, we present an Improved version of IntervalValued Intuitionistic Fuzzy Set-Weighted Aggregated Sum and Product Assessment (IIVIFS-WASPAS), which integrates a hybrid weight assessment model and IVIFS-WASPAS for the identification of TCSPs. IIVIFS-WASPAS addresses the uncertainty in the assessment data by converting the crisp data into IVIFS through expressing the MDF and NMDF in terms of intervals rather than precise numbers. Fig. 1 presents the workflow of IIVIFS-WASPAS, the proposed cloud service selection approach. The working of IIVIFS involves three phases: (i) Determine the performance of CSPs — The performance ratings of CSPs (Alternatives) for each QoS attributes are expressed in IVIFS/IVIFNs, (ii) Compute the weights of the QoS attributes — Assess the information about the importance of QoS attributes through the integrating the subjective and objective weights and (iii) Obtain the ranking order of CSPs — Rank CSPs and identify the TCSPs. 4.2.1. Phase 1: Determine the performance of CSPs with respect to the QoS attributes ( Consider a cloud service selection) problem with k CSPs Ṗi = {S1 , S2 , . . . , Sk } , ∀ i = 1, 2, . . . , k , which are assessed on ( the basis of l QoS attributes (QoS attributes) Ṡj = {C1 , C2 , . . . , Cl } , ∀j = 1, 2, . . . , l). The first phase of IIVIFS focuses on the evaluation of different QoS attributes (Criteria) and CSPs (Alternatives) for the identification of TCSPs. In simpler terms, the major objective of the first phase is to assess the performance of a multitude
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
97
Table 1 User’s preference attitude towards information and their corresponding values [59]. S.no.
Decision maker’s preference attitude
Parameter (ρ) value
1.
The negative information is absolutely preferred (NAP)
0
2.
The negative information is extremely preferred (NEP)
0.1
3.
The negative information is strongly preferred (NSP)
0.2
4.
The negative information is moderately preferred (NMP)
0.3
5.
The negative information is slightly preferred (NSP)
0.4
6.
The decision maker is neutral to the positive and negative information (NPN)
0.5
7.
The positive information is slightly preferred (PSP)
0.6
8.
The positive information is moderately preferred (PMP)
0.7
9.
The positive information is strongly preferred (PSP)
0.8
10.
The positive information is extremely preferred (PEP)
0.9
11.
The positive information is absolutely preferred (PAP)
1
Table 2 Conversion of crisp values into IVIFS [60]. Normalized crisp numbers (CN )
IVIFS
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
([0.065, 0.165] , [0.815, 0.835]) ([0.155, 0.255] , [0.725, 0.745]) ([0.245, 0.345] , [0.635, 0.655]) ([0.335, 0.435] , [0.545, 0.565]) ([0.425, 0.525] , [0.455, 0.475]) ([0.515, 0.615] , [0.365, 0.385]) ([0.605, 0.705] , [0.275, 0.295]) ([0.695, 0.795] , [0.185, 0.205]) ([0.785, 0.885] , [0.095, 0.115]) ([0.875, 0.975] , [0.005, 0.025])
of CSPs (Level-3) with respect to the several QoS attributes (Level 2) for the identification of TCSPs (Level 1-Goal) ( ) (Fig. 2). The performance ( ) matrix of each CSP Ṗi with respect to the QoS attributes Ṡj is expressed in IVIFS and an IVIFS performance matrix is constructed as detailed below: Step-1.1: Conversion of crisp data into IVIFS. In general, the cloud consumers express their preferences (feedbacks) for the quantitative attributes of the CSPs in terms of crisp values. This often leads to poor evaluation, loss of information, and less ranking accuracy. To overcome the challenges related to fuzziness and uncertainty in the data, we convert the crisp values to IVIFS (Algorithm 1). The quantitative attributes expressed ([ in the form ]) ] [ of crisp − . numbers are converted into IVIFN, Rij = Fij+ , Fij− , L+ ij , Lij [ + −] [ + −] The intervals Fij , Fij and Lij , Lij represent the MDF (degree of satisfaction) and NMDF (degree of dissatisfaction) of [ the CSPs ] (Ṗi ) on the quantitative attribute (Ṡj ), which satisfies Fij+ , Fij− ∈ [ ] − [0, 1] , L+ ∈ [0, 1] and Fij− + L− ij , Lij ij ≤ 1. Table 2 presents the conversion of crisp numbers to their corresponding IVIFS. Step-1.2: Formulate the IVIFS performance matrix with a set of CSPs (CSP 1 , CSP 2 , . . . , CSP m ) and QoS attributes ((A1 , A2), . . . , A(n ). ) Construct the IVIFS performance matrix IVIFSij k⤫l = Ƿij k⤫l , i = 1, 2, . . . , k; j = 1, 2, . . . , l with k CSPs ( ) and l QoS attributes. The IVIFS performance matrix IVIFSij k⤫l represents the performance index of ith cloud service provider to the jth attribute as defined in (Eq. (25)).
( The ) performance index of each CSP w.r.t each QoS attribute Ƿij is normalized in the range of [0,1] and then converted into respective IVIFS representation. Step-1.3: Normalize the IVIFS performance matrix. Normalization forms the integral and most important step in the evaluation of CSPs for effective decision making. It reduces the impact of high valued heterogeneous QoS attributes by transforming them in the range of [0,1]. The QoS attributes are assumed as benefit attributes ) ) an accurate ranking. The IVIFS perfor(( to obtain mance matrix IVIFSij k⤫l is normalized to balance the physical dimensions of the preference indices with respect to the various (( ) QoS attributes. ( ) ) The normalized IVIFS performance matrix ˜ ij ˜ R = Ƞ is computed using Eq. (26). k⤫l k⤫l
(
˜ ij Ƞ
)
=
([
k⤫l
] [
] [
+ ˜ − + ˜ − ˜ ˜+ ˜− ˜ U ij , Uij , Nij , Nij , Hij , Hij
+ ˜ where, U ij
])
(26) k⤫l
U+ ij
=
√
((
∑m
i =1
U+ ij
)2 ( )2 ) ; ∀ i + U− ij U− ij
− ˜ √ j = 1, 2, . . . , l; U ij =
∑m
((
∑m
((
U+ ij
i=1
)2 ( )2 ) ; ∀ i + U− ij
N+ ij
˜+ = √ j = 1, 2, . . . , l; N ij
N+ ij
i=1
N− ij
˜− = √ j = 1, 2, . . . , l; N ij ∑m
i=1
((
N+ ij
)2 ( )2 ) ; ∀ i + N− ij
)2 ( )2 ) ; ∀ i + N− ij
1, 2, . . . , k;
=
= 1, 2, . . . , k; = 1, 2, . . . , k;
= 1, 2, . . . , k; j =
− ˜+ = 1 − U ˜ ˜− 1, 2, . . . , l; H ij ij − Nij ; ∀ i = 1, 2, . . . , k; j = 1, 2, . . . , l;
˜ =1−U ˜−N ˜ ; ∀ i = 1, 2, . . . , k; j = 1, 2, . . . , l H ij ij ij −
+
+
4.2.2. Phase 2-compute weights for each QoS attributes The procedure to determine the weights of the QoS attributes is a significant method since it only has an impact on the CSPs ranking obtained by any MCDM method. The effectiveness of the proposed approach mainly depends on the defined set of QoS attributes through which the evaluation and selection of the CSPs are conducted. The proposed approach employs the integrated objective and subjective weight assessment approach
98
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Fig. 1. IIVIFS-WASPAS framework for cloud service provider selection.
Fig. 2. Hierarchical structure of cloud service provider selection.
to obtain the optimal weights of the QoS attributes. For the same, an improved version of Interval-Valued Intuitionistic Fuzzy Set-Shannon Entropy (IVIFS-SE), an objective weight assessment approach was designed to determine the objective weights of the
QoS attributes. The major motive behind the application of IVIFSSE is that the inclusion of hesitancy degree refines the arithmetic mean and acts as a better representative of the QoS attributes.
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
(
)
( )
IVIFSij k⤫l = Ƿij k⤫l =
⎛
− + − + − U+ ij , Uij , Nij , Nij , Hij , Hij
([
] [
] [
A1
]) k⤫l
A2
⎛ [ ] ⎞ ⎜ ⎜ T+ , T− , ⎜ ⎝ [ 11 11 ] ⎠ ⎜ + − ⎜ L11 , L11 ⎜ ⎜ ⎛ [ ] ⎞ ⎜ + − ⎜ T21 , T21 , ⎜ ⎝ ⎜ [ + ] ⎠ − ⎜ L21 , L21 ⎜ ⎜ . ⎜ . ⎜ . ⎜ ⎛ [ ⎜ ] ⎞ + − ⎜ T , =⎜ i1 Ti1 , ⎝ [ ⎜ ] ⎠ ⎜ + − ⎜ Li1 , Li1 ⎜ ⎜ . ⎜ . ⎜ . ⎜ ⎛ [ ] ⎞ ⎜ + ⎜ T(k−1)1 , T− (k−1)1 , ⎜ ⎝ ⎜ [ + ] ⎠ − ⎜ L(k−1)1 , L(k−1)1 ⎜ ⎜ ⎛ [ ] ⎞ ⎜ ⎜ T+ , T− , ⎝ ⎝ [ k1 k1 ] ⎠ + − Lk1 , Lk1
⎛ [ ⎝ [
T+ 12 , T12 ,
⎞
⎛ [ ···
] ⎠ −
+
T22 , T22 , +
−
]
⎞ ···
] ⎠ −
+
. . .
⎝ [
..
T+ i2 , Ti2 ,
] −
··· ..
]
⎞
L(k−1)2 , L(k−1)2
] ⎠
− T+ (k−1)2 , T(k−1)2 , +
−
⎛ [
]
⎝ [
− T+ k2 , Tk2 ,
⎝ [
···
⎞
T+ ij , Tij ,
···
···
Lij , Lij
..
]
⎞
L(k−1)j , L(k−1)j
] ⎠
− T+ (k−1)j , T(k−1)j ,
···
+
−
⎛ [
]
⎝ [
− T+ kj , Tkj ,
Lkj , Lkj +
+
−
]
⎞
Li(l−1) , Li(l−1)
] ⎠
Ti(l−1) , Ti(l−1) ,
⎝ [
+
−
+
−
⎝ [
]
⎞
Li(k−1) , Li(l−1)
] ⎠
− T+ i(k−1) , Ti(l−1) , +
−
]
⎞
L(k−1)(l−1) , L(k−1)(l−1)
] ⎠
− T+ (k−1)(l−1) , T(k−1)(l−1) ,
⎝ [
+
⎛ [ ···
⎝ [
−
]
⎞
Lk(l−1) , Lk(l−1)
] ⎠
− T+ k(l−1) , Tk(l−1) , +
−
T+ 1l , T1l ,
] −
⎞
⎟ ⎟ ⎟ ⎟ + ⎟ L1l , L1l ⎟ ⎟ ⎛ [ ⎞ ] ⎟ + − ⎟ T2l , T2l , ⎟ ⎝ [ ⎠ ⎟ ] + − ⎟ L2l , L2l ⎟ ⎟ . ⎟ . ⎟ . ⎟ ⎞ ⎛ [ ⎟ ] − ⎟ , , T T+ ⎟ il il ⎠ ⎝ [ ⎟ ] ⎟ + − ⎟ Lil , Lil ⎟ ⎟ . ⎟ . ⎟ . ⎛ [ ⎞ ⎟ ] ⎟ + − ⎟ T(k−1)l , T(k−1)l , ⎟ ⎝ [ ] ⎠ ⎟ + − ⎟ L(k−1)l , L(k−1)l ⎟ ⎟ ⎛ [ ] ⎞ ⎟ + − ⎟ Tkl , Tkl , ⎠ ⎝ [ ⎠ ] + − Lkl , Lkl ⎝ [
. . .
⎛ [ ···
⎛ [
. . .
.
⎞
] ⎠ −
L1(l−1) , L1(l−1)
] ⎠
− T+ 1(l−1) , T1(l−1) ,
⎛ [
. . .
⎝ [
⎝ [
.
⎞
] ⎠ −
+
⎞
⎛ [
..
] −
⎛ [
Lk2 , Lk2 +
]
] ⎠ −
+
.
⎞
] ⎠ −
T2j , T2j , −
. . .
Li2 , Li2 +
···
⎞
Al
]
⎛ [
L2j , L2j
⎛ [
] ⎠ −
⎞
] ⎠ −
+
.
⎞
. . .
⎝ [
⎝ [
T+ 1j , T1j ,
+
Al −1
···
] −
L1j , L1j
⎛ [
L22 , L22
⎛ [
⎛ [
⎝ [
L12 , L12
⎛ [ ⎝ [
Aj
···
] −
99
] ⎠ −
(25)
Box I.
IVIFS-SE can be expressed as in Eq. (27).
(
Ej =
−
−
m ˜ ˜ ˜ 1 ∑ Uij − Nij − Hij
m
−
)
+ ˜ij + − H ˜ij + + U˜ij − N
2
i=1
WjO = ∑n
(
1 − Ej
j=1
(
1 − Ej
);
n ∑
Wj = 1
) (27)
(28)
j=1
Where, Ej and Wj is the entropy value and weight of the attribute respectively. A smaller entropy value represents a high
entropy weight, and a greater entropy value represents a low entropy weight. Further, the ranking of the objective weights was taken as an input to determine the subjective weights of the QoS attributes. For the same, rank-order centroid, a subjective weight method was used since it reduces the maximum error of each QoS attribute weight via. ascertaining the centroid of all possible QoS attributes weights and maintains the rank order of objective weight method. Suppose there are n attributes, then the attribute ranked at jth position has the weight value mentioned in Eq. (29).
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
WjS =
Table 3 Crisp performance matrix CSP15×4 .
n 1∑ 1
n
(29)
rk
k=j
The integrated weights of the QoS attributes were computed using Eq. (30). It reflects the subjective considerations of the Decision Maker (DM) and the objective information. Wj = m ∗ WjO + n ∗ WjS
(30)
where, Wj indicates the integrated weight of the attribute; m and n represents the objective and subjective weights of the attributes and m, n ∈ [0, 1] respectively. In general, the attribute weight reflects the degree of importance of each attribute in evaluating the performance of each CSP in the cloud service selection problem. Higher weight of the attribute indicates high probability i.e., most important attribute. 4.2.3. Phase 3-ranking CSPs The ranking phase of IIVIFS-WASPAS uses WASPAS method to rank the CSPs due to its ability to provide accurate CSP ranking in various selection problems like supplier selection, logistic selection, hotel selection, etc. The WASPAS approach is a generalized approach of WSM and WPM methods. The steps involved in the WASPAS for service ranking are detailed below: Step-1: Compute the Relative Importance of ith CSP based on the WSM and WPM: The total relative importance of the ith CSP based on WSM and WPM is calculated using Eqs. (31) and (32) respectively. n ∑
WSMi = Pi =
˜ ij .Wj = Ƞ
n ∑ ([
j=1
´+ ´− ´+ ´− ´+ ´− U ij , Uij , Nij , Nij , Hij , Hij
] [
] [
])
j=1
(31)
´+ where, U = 1− ij
(
˜− Wj 1 − T ij
(
) + δ
(
˜ ij Wj 1 − T
))1/δ
)δ
))1/δ
´− , U = 1− − Wj − 1 ij ( ( ) ( ))1/δ δ = Wj L˜ + − Wj − 1 , ij
(
( ´+ − Wj − 1 , N ij ( ( ) ) 1 / δ ( ) δ − − ´ ij = Wj L˜ ij − Wj − 1 ´− ´ ij+ = 1 − U´ − ´+ N ,H ij − Nij and Hij = ´+ ´+ 1−U ij − Nij (
n ( )Wj ∏ ˜ ij Ƞ
WPMi = Ji =
j=1
=
n ([ ∏
] [ ] [ ]) + − + − Uij , Uij , Nij , Nij , Hij , Hij +
−
(32)
CSPs
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
QoS attributes/Attributes/Criteria AV
RT
P
S
SS
F
Eu
TS
CS
5 5 3 5 5 5 4 5 3 5 2 5 3 5 5
5 5 3 4 5 5 4 5 4 4 3 4 3 5 5
5 5 3 4 5 5 4 5 4 4 2 4 3 4 4
3 4 4 4 5 5 4 5 3 1 3 5 3 5 5
5 4 5 3 4 5 4 5 4 4 3 5 2 5 4
5 5 2 4 5 5 5 5 3 4 3 5 3 5 4
5 5 2 5 5 5 5 5 5 1 3 5 3 5 5
5 5 2 5 5 5 4 4 4 1 2 4 4 5 5
5 5 2 5 5 5 4 4 4 1 3 4 3 5 5
Table 4 Normalized crisp performance matrix. CSPs
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
QoS attributes/ Attributes/Criteria AV
RT
P
S
SS
F
EU
TS
CS
1 1 0.6 1 1 1 0.8 1 0.6 1 0.4 1 0.6 1 1
1 1 0.6 0.8 1 1 0.8 1 0.8 0.8 0.6 0.8 0.6 1 1
1 1 0.6 0.8 1 1 0.8 1 0.8 0.8 0.4 0.8 0.6 0.8 0.8
0.6 0.8 0.8 0.8 1 1 0.8 1 0.6 0.2 0.6 1 0.6 1 1
1 0.8 1 0.6 0.8 1 0.8 1 0.8 0.8 0.6 1 0.4 1 0.8
1 1 0.4 0.8 1 1 1 1 0.6 0.8 0.6 1 0.6 1 0.8
1 1 0.4 1 1 1 1 1 1 0.2 0.6 1 0.6 1 1
1 1 0.4 1 1 1 0.8 0.8 0.8 0.2 0.4 0.8 0.8 1 1
1 1 0.4 1 1 1 0.8 0.8 0.8 0.2 0.6 0.8 0.6 1 1
transformed into WSM and WPM respectively
⏐ ⏐ ⏐∑ ⏐ ⏐ ⏐ ⏐ Ji ⏐ ⏐ ⏐ ⏐⏐ ƥ = ⏐0.5 − ⏐∑ ∑ ⏐ .Pi + Ji ⏐ ⏐ ⏐
(34)
Step-3: Rank the CSPs. The preference attitude of the decision experts reflected by the preference attitudinal score and accuracy degree is computed (Eqs. (24) and (20)) and the CSPs are ranked in decreasing order, i.e., rank 1 represents the trustworthy CSP.
j=1
( ( )δ ( ))1/δ − ˜− − Wj − 1 , Uij = Wj T − ij ( ) 1 /δ ( ) ( ) ( ))1/δ + δ ˜+ Wj − 1 , Nij = 1 − Wj 1 − L − Wj − 1 , N− ij ij = ( ( ) 1 / δ )δ ( ) − + − − ˜ ij − Wj − 1 1 − Wj 1 − L , Hij = 1 − Uij − Nij and where, U+ = ij
−
+
(
˜+ Wj T ij
(
)δ
+
Hij = 1 − Uij − Nij . The summation and product of all the attributes are computed using Schweizer-Sklar operations (Eqs. (5)–(7)). Step-2: Calculate the total relative importance for each CSP (alternative). A generalized criterion of WASPAS is calculated based on the additive method of WSM and the multiplicative method of WPM for each CSP using Eq. (33).
WASPASi = Yi
= ƥ. Pi + (1 − ƥ) Ji =
([
− − U+ , N+ , Hi+ , Hi− i , Ui i , Ni
] [
] [
])
(33)
Where, ƥ is the parameter of the WASPAS method (Eq. (34)) and ƥ ∈ [0, 1]. If ƥ = 1 and ƥ = 0, the WASPAS method is
5. Case study The performance of IIVIFS-WASPAS, the proposed cloud service selection methodology has been evaluated using a sample dataset extracted from the Cloud Armor project, University of Adelaide [61], a real-world trust feedback dataset which focus on the development of a robust trust management framework for the cloud environment. It contains 10,080 user feedbacks for nine QoS attributes (Benefit attribute: Availability (AV), Response Time (RT), Security (Sec), Speed (S), Storage Space (SS), Features (F), Ease-of-use (Eu), Technical Support (TS), Customer Service (CS) and Level of Expertise (LoE); Cost attribute: Price (P)) provided by nearly 7000 consumers for 114 real-world cloud services. The user feedbacks were obtained from the major review websites like Cloud Hosting Reviews, Cloud Service Providers, Cloud Storage Reviews, and Ratings during the period July 2003 to June 2012 at different timestamps. The sample trust feedback dataset considered for the case study comprises users’ feedbacks for fifteen CSPs namely,
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
101
Table 5 IVIFS performance matrix (IVIFS 15×9 ). CSPs
QoS attributes AV
RT
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.515, 0.615] , [0.365, 0.385]
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{ CSP1
{ CSP2 CSP3 CSP4 CSP5
{ CSP6
{ CSP7
{ CSP8
{ CSP9
{ CSP10 CSP11 CSP12
{ CSP13
{ CSP14
{ CSP15 CSPs/Alternatives
}
}
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.875, 0.975] , [0.005, 0.025]
}
}
}
}
TS
CS
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.515, 0.615] , [0.365, 0.385]
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.695, 0.795] , [0.185, 0.205]
[0.695, 0.795] , [0.185, 0.205]
{
[0.155, 0.255] , [0.725, 0.745]
{
[0.155, 0.255] , [0.725, 0.745]
{
[0.155, 0.255] , [0.725, 0.745]
[0.515, 0.615] , [0.365, 0.385]
{
[0.515, 0.615] , [0.365, 0.385]
{
[0.335, 0.435] , [0.545, 0.565]
{
[0.515, 0.615] , [0.365, 0.385]
CSP4
{ { { { { { { CSP11
{
[0.875, 0.975] , [0.005, 0.025]
CSP3
CSP10
}
EU
{
CSP9
[0.875, 0.975] , [0.005, 0.025]
{
CSP2
CSP8
{
}
CSP1
CSP7
SS
) [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.155, 0.255] , [0.725, 0.745] { } [0.515, 0.615] , [0.365, 0.385] { } [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] (
[0.875, 0.975] , [0.005, 0.025]
{
CSP6
S
} [0.875, 0.975] , [0.005, 0.025] ( ) [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.335, 0.435] , [0.545, 0.565] { } [0.695, 0.795] , [0.185, 0.205] { } [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205]
Criteria/Attributes F
CSP5
P
{
}
}
}
}
}
}
}
}
}
}
}
}
(continued on next page)
102
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Table 5 (continued). CSPs/Alternatives
Criteria/Attributes F
EU
[0.875, 0.975] , {[0.005, 0.025] } [0.515, 0.615] , [0.365, 0.385]
{
CSP12 CSP13
TS
}
[0.875, 0.975] , {[0.005, 0.025] } [0.515, 0.615] , [0.365, 0.385]
{
CS
}
[0.695, 0.795] , {[0.185, 0.205] } [0.695, 0.795] , [0.185, 0.205]
{
}
[0.695, 0.795] , {[0.185, 0.205] } [0.515, 0.615] , [0.365, 0.385]
{
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
CSP14 CSP15
Table 6 Normalized IVIFS performance matrix (IVIFS 15×9 ). CSPs
CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
QoS attributes AV
RT
P
SP
SS
⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1535, 0.1755] ,⎬ [0.1489, 0.1650] , ⎩[0.6594, 0.6976] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎫ ⎧ ⎨[0.0740, 0.0961] ,⎬ [0.4387, 0.4548] , ⎩[0.4492, 0.4873] ⎭ ⎫ ⎧ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎫ ⎧ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭
⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎫ ⎧ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭
⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1215, 0.1451] ,⎬ [0.2786, 0.2939] , ⎩[0.5611, 0.5999] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.0790, 0.1026] ,⎬ [0.4160, 0.4313] , ⎩[0.4661, 0.5050] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎫ ⎧ ⎨[0.1215, 0.1451] ,⎬ [0.2786, 0.2939] , ⎩[0.5611, 0.5999] ⎭ ⎫ ⎧ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭
⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭ ⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.0371, 0.0611] ,⎬ [0.4571, 0.4697] , ⎩[0.4692, 0.5057] ⎭ ⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎫ ⎧ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭ ⎫ ⎧ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭
⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1195, 0.1427] ,⎬ [0.2850, 0.3006] , ⎩[0.5567, 0.5955] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎫ ⎧ ⎨[0.1195, 0.1427] ,⎬ [0.2850, 0.3006] , ⎩[0.5567, 0.5955] ⎭ ⎫ ⎧ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.0777, 0.1009] ,⎬ [0.4255, 0.4411] , ⎩[0.4580, 0.4968] ⎭ ⎫ ⎧ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ (continued on next page)
Backupgenie (CSP1 ), Bluehost (CSP2 ), Carbonite (CSP3 ), Elephantdriv e (CSP4 ), GoDaddy (CSP5 ), ibackup (CSP6 ), idriv e (CSP7 ), justcloud (CSP8 ), keepit (CSP9 ), liv edriv e (CSP10 ), Mozy (CSP11 ), MyPCBackup (CSP12 ), sos − online − backup (CSP13 ), SugarSync (CSP14 ), and
yousendit − online − backup (CSP15 ) provided for nine QoS attributes namely, AV , RT , P , S , SS , F , Eu, TS and CS. The user feedback ranges from 1 to 5, where 1 represents the most insignificant feedback and 5 represents the most significant feedback. For the construction of a complete user-service trust feedback
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
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Table 6 (continued). CSPs
QoS attributes AV
RT
P
SP
SS
CSP15
⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭
⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭
⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭
⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭
⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭
CSPs
CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
CSP15
QoS attributes F
Eu
TS
CS
⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.0762, 0.0990] ,⎬ [0.4187, 0.4340] , ⎩[0.4670, 0.5051] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1421, 0.1575] , ⎩ ⎭ ⎧[0.6616, 0.6997] ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1575, 0.1421] , ⎩[0.6770, 0.6843] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎫ ⎧ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1575, 0.1421] , ⎩[0.6770, 0.6843] ⎭
⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.0739, 0.0959] ,⎬ [0.3620, 0.3753] , ⎩[0.5288, 0.5641] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩ ⎭ ⎧[0.7683, 0.8037] ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.0342, 0.0562] ,⎬ [0.4815, 0.4948] , ⎩[0.4490, 0.4843] ⎭ ⎧ ⎫ ⎨[0.1136, 0.1356] ,⎬ [0.2424, 0.2557] , ⎩[0.6086, 0.6440] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1136, 0.1356] ,⎬ [0.2424, 0.2557] , ⎩[0.6086, 0.6440] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎫ ⎧ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭
⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.0784, 0.1017] ,⎬ [0.3317, 0.3439] , ⎩[0.5543, 0.5899] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎭ ⎩ ⎧[0.7567, 0.7923] ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.0363, 0.0596] ,⎬ [0.4413, 0.4535] , ⎩[0.4869, 0.5224] ⎭ ⎧ ⎫ ⎨[0.0784, 0.1017] ,⎬ [0.3317, 0.3439] , ⎩[0.5543, 0.5899] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎫ ⎧ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭
⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.0786, 0.1021] ,⎬ [0.3400, 0.3525] , ⎩[0.5454, 0.5814] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩ ⎭ ⎧[0.7556, 0.7915] ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.0364, 0.0599] ,⎬ [0.4523, 0.4648] . ⎩[0.4754, 0.5113] ⎭ ⎧ ⎫ ⎨[0.1209, 0.1444] ,⎬ [0.2277, 0.2402] , ⎩[0.6155, 0.6514] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1209, 0.1444] ,⎬ [0.2277, 0.2402] , ⎩[0.6155, 0.6514] ⎭ ⎫ ⎧ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭
Table 7 Entropy values and weights for each attribute. Ej Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.6445 0.1117 4
0.6410 0.1128 1
0.6429 0.1122 2
0.6488 0.1103 6
0.6432 0.1121 3
0.6445 0.1117 5
0.6502 0.1099 7
0.6515 0.1095 9
0.6503 0.1099 8
dataset, the feedback entries with missing values and redundant CSPs feedback entries were removed. The degree of dependency among the QoS attributes was checked using the chi-square test with (r − 1, c − 1) degrees of freedom where, r represents the
number of cloud service providers and c represents the number of QoS attributes.
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 8 Subjective weights for each attribute. Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.1342 4
0.2002 1
0.1783 2
0.0900 6
0.1563 3
0.1121 4
0.0676 7
0.0226 9
0.0451 8
Table 9 The integrated weights for each attribute and their ranking. Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.1229 4
0.1565 1
0.1452 2
0.1002 6
0.1342 3
0.1119 5
0.0887 7
0.0660 9
0.0775 8
Table 10 IVIFS-WSM and IVIFS-WPM for cloud service providers. CSPs CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
CSP15
IVIFS-WSM (Pi )
IVIFS-WPM (Ji )
IVIFS-WASPAS
⎧ ⎫ ⎨[0.1939, 0.2169] ,⎬ [0.0039, 0.0196] , ⎩[0.7634, 0.8022] ⎭ ⎧ ⎫ ⎨[0.1922, 0.2152] ,⎬ [0.0042, 0.0211] , ⎩[0.7637, 0.8036] ⎭ ⎧ ⎫ ⎨[0.1233, 0.1465] ,⎬ [0.0106, 0.0523] , ⎩[0.8012, 0.8661] ⎭ ⎧ ⎫ ⎨[0.1702, 0.1933] ,⎬ [0.0057, 0.0283] , ⎩[0.7700, 0.8241] ⎭ ⎧ ⎫ ⎨[0.1964, 0.2194] ,⎬ [0.0039, 0.0194] , ⎩[0.7611, 0.7997] ⎭ ⎧ ⎫ ⎨[0.2017, 0.2247] ,⎬ [0.0037, 0.0183] , ⎩[0.7570, 0.7947] ⎭ ⎧ ⎫ ⎨[0.1687, 0.1197] ,⎬ [0.0080, 0.0389] , ⎩[0.7694, 0.8233] ⎭ ⎧ ⎫ ⎨[0.1959, 0.2190] ,⎬ [0.0041, 0.0204] , ⎩[0.7606, 0.8000] ⎭ ⎧ ⎫ ⎨[0.1509, 0.1740] ,⎬ [0.0111, 0.534] , ⎩[0.7726, 0.8379] ⎭ ⎧ ⎫ ⎨[0.1297, 0.1528] ,⎬ [0.0115, 0.0554] , ⎩[0.7917, 0.8589] ⎭ ⎧ ⎫ ⎨[0.1055, 0.1286] ,⎬ [0.2950, 0.3102] , ⎩[0.5612, 0.5995] ⎭ ⎫ ⎧ ⎨[0.1838, 0.2068] ,⎬ [0.0049, 0.0242] , ⎩[0.7690, 0.8114] ⎭ ⎧ ⎫ ⎨[0.1165, 0.1395] ,⎬ [0.2425, 0.2594] , ⎩[0.6011, 0.6410] ⎭ ⎧ ⎫ ⎨[0.1958, 0.2188] ,⎬ [0.0039, 0.0196] , ⎩[0.7616, 0.8003] ⎭ ⎧ ⎫ ⎨[0.1860, 0.2090] ,⎬ [0.0045, 0.0226] , ⎩[0.7684, 0.8095] ⎭
⎧ ⎫ ⎨[0.1852, 0.2095] ,⎬ [0.0359, 0.0508] , ⎩[0.7397, 0.7789] ⎭ ⎧ ⎫ ⎨[0.1887, 0.2120] ,⎬ [0.0392, 0.0543] , ⎩[0.7337, 0.7721] ⎭ ⎧ ⎫ ⎨[0.1018, 0.1271] ,⎬ [0.2944, 0.3099] , ⎩[0.5630, 0.6038] ⎭ ⎧ ⎫ ⎨[0.1616, 0.1855] ,⎬ [0.1295, 0.1451] , ⎩[0.6693, 0.7089] ⎭ ⎧ ⎫ ⎨[0.1934, 0.2165] ,⎬ [0.0267, 0.0419] , ⎩[0.7416, 0.7799] ⎭ ⎧ ⎫ ⎨[0.2006, 0.2236] ,⎬ [0.0038, 0.0188] , ⎩[0.7576, 0.7956] ⎭ ⎧ ⎫ ⎨[0.1659, 0.1891] ,⎬ [0.1180, 0.1333] , ⎩[0.6777, 0.7161] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2162] ,⎬ [0.0223, 0.0372] , ⎩[0.7466, 0.7847] ⎭ ⎧ ⎫ ⎨[0.1430, 0.1668] ,⎬ [0.1852, 0.2006] , ⎩[0.6326, 0.6718] ⎭ ⎧ ⎫ ⎨[0.0596, 0.0936] ,⎬ [0.2961, 0.3112] , ⎩[0.5952, 0.6444] ⎭ ⎧ ⎫ ⎨[0.0979, 0.1221] ,⎬ [0.3319, 0.3475] , ⎩[0.5303, 0.5702] ⎭ ⎫ ⎧ ⎨[0.1791, 0.2025] ,⎬ [0.0732, 0.0885] , ⎩[0.7090, 0.7477] ⎭ ⎫ ⎧ ⎨[0.1101, 0.1341] ,⎬ [0.2982, 0.3138] , ⎩[0.5521, 0.5917] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2162] ,⎬ [0.0279, 0.0430] , ⎩[0.7408, 0.7791] ⎭ ⎫ ⎧ ⎨[0.1814, 0.2047] ,⎬ [0.0657, 0.0809] , ⎩[0.7144, 0.7529] ⎭
⎧ ⎫ ⎨[0.1882, 0.2120] ,⎬ [0.0067, 0.0298] , ⎩[0.7582, 0.8051] ⎭ ⎧ ⎫ ⎨[0.1899, 0.2131] ,⎬ [0.0072, 0.0319] , ⎩[0.7550, 0.8029] ⎭ ⎧ ⎫ ⎨[0.1092, 0.1338] ,⎬ [0.0184, 0.0879] , ⎩[0.7783, 0.8725] ⎭ ⎧ ⎫ ⎨[0.1645, 0.1882] ,⎬ [0.0098, 0.0471] , ⎩[0.7648, 0.8257] ⎭ ⎧ ⎫ ⎨[0.1944, 0.2175] ,⎬ [0.0066, 0.0281] , ⎩[0.7544, 0.7990] ⎭ ⎧ ⎫ ⎨[0.2010, 0.2240] ,⎬ [0.0037, 0.0186] , ⎩[0.7574, 0.7953] ⎭ ⎧ ⎫ ⎨[0.1668, 0.1899] ,⎬ [0.0137, 0.0621] , ⎩[0.7479, 0.8194] ⎭ ⎧ ⎫ ⎨[0.1940, 0.2171] ,⎬ [0.0068, 0.0279] , ⎩[0.7550, 0.7992] ⎭ ⎧ ⎫ ⎨[0.1457, 0.1692] ,⎬ [0.0191, 0.0863] , ⎩[0.7444, 0.8352] ⎭ ⎧ ⎫ ⎨[0.0849, 0.1148] ,⎬ [0.0198, 0.0929] , ⎩[0.7923, 0.8953] ⎭ ⎧ ⎫ ⎨[0.1005, 0.1243] ,⎬ [0.3180, 0.3335] , ⎩[0.5421, 0.5815] ⎭ ⎧ ⎫ ⎨[0.1807, 0.2039] ,⎬ [0.0084, 0.0390] , ⎩[0.7570, 0.8109] ⎭ ⎫ ⎧ ⎨[0.1123, 0.1360] ,⎬ [0.2755, 0.2919] , ⎩[0.5721, 0.6123] ⎭ ⎫ ⎧ ⎨[0.1940, 0.2171] ,⎬ [0.0066, 0.0285] , ⎩[0.7544, 0.7994] ⎭ ⎧ ⎫ ⎨[0.1829, 0.2062] ,⎬ [0.0078, 0.0363] , ⎩[0.7575, 0.8093] ⎭
(i) Construction of IVIFS Performance Matrix Initially, the performance matrix (CSP15×9 ) was generated for fifteen cloud service providers (Alternatives) and nine QoS attributes (Criteria) using the crisp numbers (Table 3). The crisp
performance matrix (CSP15×9 ) in Table 3 was converted into normalized crisp values (Table 4).
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 11 Cloud service providers ranking. CSPs
degree (Score ) Siρ (δ)
Accuracy ( ) degree Aiρ (δ)
Uncertainty ( ) degree Ui
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
0.3006 0.3005 0.1900 0.2676 0.3071 0.3197 0.2594 0.3067 0.2240 0.1665 −0.1092 0.2875 −0.0534 0.3064 0.2914
0.5939 0.5930 0.6085 0.5984 0.5922 0.5921 0.5946 0.5924 0.5966 0.6146 0.5206 0.5947 0.5307 0.5923 0.5945
0.4061 0.4070 0.3915 0.4016 0.4078 0.4079 0.4054 0.4076 0.4034 0.3854 0.4794 0.4053 0.4693 0.4077 0.4055
105
Among the nine QoS attributes, the most important QoS attributes are Response Time (RT) and Price (P), whereas the least important QoS attribute is Technical Support (TS). (iii) Compute the Relative Importance of CSPs The relative importance of the considered CSPs based on WSM (Eq. (31)), WPM (Eq. (32)) and the total relative importance of each CSP was determined using generalized WASPAS measure (Eq. (33)) (Table 10). The parameter (ƥ) value was derived using Eq. (34).
⏐ ⏐ ƥ = ⏐⏐0.5 −
1.7952
⏐ ⏐ ⏐ = |0.5 − 0.2| = 0.3 9.1139 + 1.7952 ⏐
Table 11 presents the score, accuracy and uncertainty degree (Ui =1-Aiρ (δ)) of CSPs in the range of [0, 1]. ( i The) service ranking with respect to the (i) Score degree Sρ (δ) : CSP 6 > CSP5 > CSP8 > CSP14 > CSP1 > CSP2 > CSP15 > CSP13 > CSP4 > CSP7 (> CSP9) > CSP3 > CSP10 > CSP13 > CSP11 , (ii) Accuracy degree Aiρ (δ) : CSP 10 > CSP3 > CSP4 > CSP9 > CSP12 > CSP7 > CSP15 > CSP1 > CSP2 > CSP8 > CSP ( 14 ) > CS5 > CSP6 > CSP13 > CSP11 and (iii) Uncertainty degree Ui : : CSP 10 > CSP3 > CSP4 > CSP9 > CSP12 > CSP7 > CSP15 > CSP1 > CSP2 > CSP8 > CSP14 > CS5 > CSP6 > CSP13 > CSP11 . 5.1. Performance validation The effectiveness of IIVIFS-WASPAS, the proposed cloud service selection approach over the state-of-the-art IVIFS based cloud service selection approaches was validated using a three stage empirical model in terms of cardinal ranking, sensitivity analysis, and rank reversal phenomenon.
Fig. 3. CSPs ranking acceptability indices with respect to decision mechanism coefficient.
Further, the normalized crisp performance matrix (Table 4) was converted into their corresponding IVIFN using the conversion rule given in Table 2. Table 5 presents the IVIFS performance matrix (IVIFS )15×9 for fifteen cloud service providers and nine QoS attributes. The hesitancy degree for a given MDF ( corresponding ) and NDF for IVIFSij 15×9 is [0.000, 0.120] which is obtained using Eq. (3). The IVIFS performance matrix was normalized using Eq. (26) to construct the normalized IVIFS performance matrix (IVIFS )15×9 (Table 6). (ii) Determine Weights of the QoS Attributes ( ) The objective and subjective weights of each attribute Wj was determined using modified IVIFS-SE (Eqs. (27)–(28)) and rank-centroid approach (Eq. (29)). A hybrid weight assessment model (Eq. (30)) was used to determine the weights of the QoS attributes which are then used to evaluate the CSPs for the identification of TCSPs and derive accurate service ranking. Table 7 presents the entropy values and their corresponding QoS attributes weights and rank in an increasing order. The subjective weights of the QoS attributes using the subjective weight assessment method, i.e., rank-centroid method is given in Table 8. Further, the integrated weights of the QoS attributes are given in Table 9.
5.1.1. Cardinal rankings of the state-of-the-art IVIFS based cloud service provider selection approach for the selection of TCSPs IIVIFS-WASPAS, the proposed cloud service provider selection approach which integrates a hybrid weight model and IVIFSWASPAS for the identification of TCSPs with accurate service ranking was compared with the state-of-the-art IVIFS service selection approaches like IVIFS-Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) plus full MULTIplicative form (MULTI) (IVIFS-MULTIMOORA) [36], IVIFS-TOPSIS [62], IVIFSVlsekriterijumska Optimizacija I KOmpromisno Resenje (IVIFSVIKOR) [36], and IVIFS-Complex Proportional Assessment of alternativeS (IVIFS-COPRAS) [36] based on the Spearman’s rank correlation analysis (ρr ). From Table 12, it was evident that ibackup (CSP 6 ) is the optimal trustworthy cloud service provider based on the service ranking provided by the IIVIFS and the stateof-the-art IVIFS based service selection approach. Even though, the other MCDM approaches listed in Table 12 were used to solve the cloud service selection problem they are inefficient in providing accurate service ranking on the addition or removal of the best service provider (ibackup) or the worst service provider (Mozy) respectively. Spearman’s rank correlation analysis (ρr ), a non-parametric test was employed to validate the correctness of the ranking provided by the IIVIFS and the state-of-the-art IVIFS based cloud service selection approaches (Eq. (35)).
ρr = 1 −
6
∑
d2i
m (m − 1)
(35)
Where, m is the number of alternatives, di is the difference between the ranks of any two MCDM approaches. Table 13 presents the interpretation of different values of ρr [63]. From the Table 13, it was evident that if the Spearman rank correlation (ρr ) is higher than 0.6, then there is a high statistical dependency among the considered IVIFS approaches.
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 12 Comparison of trustworthy CSPs ranking. CSPs
IIVIFSWASPAS
IVIFSMULTIMOORA [36]
IVIFSTOPSIS [62]
IVIFSVIKOR [36]
IVIFSCOPRAS [36]
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
5 6 12 9 2 1 10 3 11 13 15 8 14 4 7
5 6 13 9 2 1 10 4 11 12 15 8 14 3 7
5 6 13 9 3 1 10 2 11 12 15 8 14 4 7
6 5 13 10 3 1 9 2 11 12 15 8 14 4 7
5 6 13 9 2 1 10 4 11 12 15 8 14 3 7
Table 13 Spearman’s rank correlation analysis range. Correlation analysis range
Interpretation
0.8 0.6 0.4 0.2
Very strong Strong Average Weak Very weak
< ρr < ρr < ρr < ρr ρr ≤ 0.2
≤ 1.0 ≤ 0.8 ≤ 0.6 ≤ 0.4
Table 14 presents the rank correlation analysis between IIVIFSWASPAS and the state-of-the-art IVIFS based service selection approaches. From Table 14, it was found that the rank correlation analysis for most of the IVIFS approaches was greater than 0.7. Therefore, we state that the service ranking provided by the IIVIFS-WASPAS is consistent with the considered IVIFS-MCDM based service selection approaches. 5.1.2. Sensitivity analysis In order to increase accuracy and efficiency of the IIVIFSWASPAS, the impact of the change in coefficient (ƥ) value is examined. The coefficient (ƥ) value was computed using Eq. (34) which lies in the range of [0, 1] with the step size of 0.1. Fig. 3 represents the relative values of the CSPs by varying the coefficient value (from ƥ = 0.1 to ƥ = 1) while retaining the same QoS attributes weights in order to obtain stability of CSP ranking. The service ranking obtained by varying the coefficient (ƥ) value (from 0 to 1) was ordered as ibackup > justcloud > GoDaddy > SugarSync > Backupgenie > Bluehost > MyPCBackup > Yousendit − online − backup > Elephantdriv e > idriv e > Keepit > Carbonite > Liv edriv e > Sos − online − backup > Mozy. The relative values of the fifteen CSPs increase by 0.0821, 0.0829, 0.09, 0.0832, 0.0825, 0.0824, 0.0846, 0.0827, 0.0871, 0.0894, 0.0929, 0.0825, 0.0914, 0.0816, and 0.0822 with the increase in the ƥ value. From the above series of improvement in the relative values of CSPs, we conclude that ibackup(CSP 6 ) is the trustworthy cloud service provider since it has the minimal fluctuations in the relative value. Subsequently, the sensitivity analysis has been carried by varying the different criterion weights in order to maintain the robustness of the proposed methodology (IIVIFS-WASPAS). For instance, the CSP ranking does not vary on interchanging the weights C1 with C2 while keeping the weights of the remaining criteria (C3 to C9 ) as constant. Similarly, the weights of the other criteria can be interchanged and their respective impact on the service ranking can be analysed. Fig. 4 demonstrates the sensitivity of the CSP ranking to the changes in the weights of the QoS attributes for 4 cases (C 1 − C 2, C 2 − C 8, C 3 − C 7 and C 3 − C 4).
5.1.3. Rank Reversal Phenomenon (RRP) In the literature, several MCDM approaches have been used for effective decision making for the identification of TCSPs. Despite the advantages of these approaches, they are inefficient in preventing the Rank Reversal Phenomenon (RRP) due to mutual correlation(s) among the relevant and irrelevant CSPs, i.e., change in the set of candidate CSPs. This is due to the use of improper normalization technique [64] in several MCDM methods like AHP (Min–max normalization), PROMETHEE (Preference Ranking Organization Method of Enrichment Evaluations-linear normalization), TOPSIS (vector normalization), ELECTRE (Elimination and Choice Expressing REality-linear normalization), MULTIMOORA (target-based normalization), DEA (Data Envelopment Analysislinear normalization), etc. IIVIFS-WASPAS, the proposed service selection approach addresses the RRP problem through proximity index and thereby obtains consistent ranking by minimizing the RRP. For instance, the preference/ranking order of cloud service providers remains same after the addition of best service provider (ibackup) and/or the deletion of an existing service provider (Liv edriv e). Fig. 5 presents the ranking of fourteen CSPs after the removal of worst CSP (Mozy). 6. Conclusions ‘Service Selection Problem’ remains a challenging research area in the field of cloud computing due to the emerging new cloud service providers with different functionalities and dynamic user requirements. Further, the uncertainty in the objective and subjective assessment data, a primary source for cloud service evaluation complicates the service selection problem. To address the same, this work presents Improved Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregated Sum and Product Assessment (IIVIFS-WASPAS) based cloud service selection approach for the identification of the trustworthy CSPs. IIVIFSWASPAS employs an integrated objective & subjective weight assessment approach and preference attitudinal score and accuracy function based IVIFS-WASPAS for weight assessment of the QoS attributes and service ranking respectively. Further, the uncertainty in the user preferences is captured by the IVIFS. The effectiveness of the IIVIFS-WASPAS cloud service provider selection approach was validated using a sample trust feedback dataset with fifteen CSPs and nine QoS attributes derived from the Cloud Armor trust feedback dataset in terms of sensitivity analysis and rank reversal phenomenon. The application of trust prediction and user-service based QoS value prediction, an integral part of any cloud service selection framework proves to be a challenging future research direction of this work.
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 14 Spearman’s rank correlation analysis. IIVIFS-WASPAS IVIFS-MULTIMOORA IVIFS-TOPSIS IVIFS-VIKOR IVIFS-COPRAS
IIVIFS-WASPAS
IVIFS-MULTIMOORA
IVIFS-TOPSIS
IVIFS-VIKOR
IVIFS-COPRA
– 0.89 0.89 0.77 0.89
0.89 – 0.83 0.71 1.00
0.89 0.83 – 0.89 0.83
0.77 0.71 0.89 – 0.71
0.89 1.00 0.83 0.71 –
Fig. 4. Robustness-Interchange of criterion weights.
Fig. 5. Ranking after the removal of worst CSP (Mozy).
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by The Council of Scientific & Industrial Research, India and The Department of Science & Technology, India (Grant No: CSIR - SRF Fellowship/143345/2K17/1 and SR/FST/ETI-349/2013). The authors gratefully acknowledge Tata Realty-IT City-SASTRA Srinivasa Ramanujan Research Cell of SASTRA Deemed University for the financial support extended to us in carrying out this research work.
Appendix
Abbreviations Abstract MCDM CSPs QoS IVIFS-WASPAS
TCSPs IIVIFS-WASPAS RRP
Explanation Multi-Criteria Decision Making Cloud Service Providers Quality of Service Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregate Sum and Product ASsessment Trustworthy CSPs Improved IVIFS-WASPAS Rank Reversal Phenomenon
107
108
1. Introduction ICT StaaS FMCDM IFS NFS HFS WSM WPM SE 2. Literature review FAHP-WASPAS NMCDA AHP 2sFL FAHP MATLAB FTOPSIS
GDM CCT PS IVIF AHP IVIF COPRAS IVIF MULTIMOORA
IVIF VIKOR FEA BSC FDM Cloud-FuSeR FLW MSER OMNeT++ CINS INS MAGDM TIFNs MCGDM FANP ELECTRE GRA ER CTE PI DI PD IVFS
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Information and Communication Technology Storage as a Service Fuzzy based MCDM Intuitionistic Fuzzy Set Neutrosophic Fuzzy Set Hesitant Fuzzy Set Weighted Sum Model Weighted Product Model Shannon Entropy Fuzzy Analytic Hierarchy Process-WASPAS Neutrosophic Multi-Criteria Decision Analysis Analytic Hierarchy Process two-stage Fuzzy Logic Fuzzy AHP MATrix LABoratory Fuzzy based Technique for Order of Preference by Similarity to Ideal Solution Group Decision Making Cloud Computing Technology Provider Selection Interval-Valued Intuitionistic Fuzzy AHP IVIF COmplex PRoportional ASsessment IVIF multi-objective optimization by ratio analysis plus the full multiplicative form IVIF VišekriterijumskoKompromisnoRangiranje Fuzzy Extent Analysis Balanced Score Card Fuzzy Delphi Method Fuzzy user-oriented cloud SeRvice selection Fuzzy LightWeight Mean Squared Error of Ranks Objective Modular Network testbed in C++ Cloud service Interval Neutrosophic Set Interval Neutrosophic Set Multi-Attribute Group Decision-Making Triangular Intuitionistic Fuzzy Numbers Multi-Criteria Group Decision Making Fuzzy Analytic Network Process Elimination and Choice Translating Reality Grey Relational Analysis Evidence Reasoning Cloud service Trustworthiness Evaluation Performance Importance Delivery Importance Performance Delivery Interval-Valued Fuzzy Set
3.1. Interval-Valued Intuitionistic Fuzzy Set (IVIFS) MDF Membership Degree Function NMDF Non-Membership Degree Function HDF Hesitant Degree Function IFN Intuitionistic Fuzzy Number HD Hesitancy Degree IVIFV Interval-Valued Intuitionistic Fuzzy Value IVIFN Interval-Valued Intuitionistic Fuzzy Number SS Schweizer-Sklar ATT Archimedean t-norm and t-conorm 4.2.2. Phase 2-Compute Weights for each QoS Attributes IVFS-SE Interval-Valued Intuitionistic Fuzzy Sets-Shannon Entropy DM Decision Maker
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Nivethitha Somu is an Institute Post Doctoral Fellow at Smart Energy Informatics Laboratory (SEIL), Department of Computer Science and Engineering, Indian Institute of Technology (IIT-B), Bombay. She was a Senior Research Fellow at Center for Information Super Highway (CISH) School of Computing, SASTRA Deemed University, Thanjavur, INDIA (2013–2018). She was awarded The Department of Science and Technology - ‘‘Innovation in Science Pursuit for Inspired Research (INSPIRE)’’ Fellowship’2013. She received her Master’s degree in Science from Anna University, Chennai, INDIA in 2011. She also received her Master’s degree in Technology from SASTRA Deemed University, Thanjavur, INDIA in 2013. She is a lifetime member of Ramanujan Mathematical Society. Her current research interests include Cloud service selection, QoS Prediction, Machine learning, Energy informatics, and Intrusion detection systems.
Obulaporam Gireesha is a Senior Research Fellow at Center for Information Super Highway (CISH) School of Computing, SASTRA Deemed University, Thanjavur, INDIA. She was awarded The Council for Scientific & Industrial Research (CSIR) - Senior Research Fellowship’ 2018. She obtained her Bachelor’s degree in Information Technology from Sri Padmavati Mahila VisvaVidyalayam (SPMVV) Women’s University, Tirupati, India in 2014. She received his Master’s degree in Software Engineering from Sree Vidyanikethan Engineering College (SVEC), Tirupati, India in 2016. She is a lifetime member of Ramanujan Mathematical Society. Her current research interests include Cloud service selection, Multi criteria decision making, and Elliptic curve cryptography.
Shankar Sriram V.S. is a Professor of Information Technology; and Chair Professor for TATA Communications — Cyber Security at School of Computing, SASTRA Deemed University, Thanjavur, Tamil Nadu, INDIA. He received his Bachelor’s degree in Science from Madurai Kamaraj University, Madurai, India. He obtained his Master’s degree in Computer Applications from Madurai Kamaraj University, Madurai, India. He also received his Master’s degree in Engineering from Thapar University, Punjab, India. He was conferred Ph.D. in Information and Network Security from Birla Institute of Technology, Mesra, India. He has been in the Academia for the past 19 years. He is a member of IEEE. He was awarded the IBM Shared University Research (SUR) Award’ 2017. His current area of research includes information and Network security, Cloud computing, Big data analytics, Machine learning, and Graph-based data mining.
Kannan Krithivasan is a Professor in the Department of Mathematics, SASTRA Deemed University, Thanjavur, INDIA. He obtained his Bachelor’s and Master’s degrees from the University of Madras, India, in 1980 and 1982, respectively. He also received his Bachelor’s and Master’s degrees in Education from Madurai Kamaraj University, India, in 1984 and 1986 respectively. He obtained his M.Phil. degree in Mathematics from Regional Engineering College, Tiruchirapalli, India, in 1988. He was conferred Ph.D. in Mathematics in the area of Computational Fluid Dynamics by Alagappa University, Karaikudi, India, in 2000. He is a member of IEEE. He is also a lifetime member of Ramanujan Mathematical Society. He has been in Academia for the past 34 years. His specific areas of interest include Combinatorial optimization, Hypergraph based image processing, and Bayesian computing.
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Future Generation Computer Systems journal homepage: www.elsevier.com/locate/fgcs
IIVIFS-WASPAS: An integrated Multi-Criteria Decision-Making perspective for cloud service provider selection Obulaporam Gireesha a , Nivethitha Somu b , Kannan Krithivasan c , Shankar Sriram V.S. a ,
∗
a
Centre for Information Super Highway (CISH), School of Computing, SASTRA Deemed University, Thanjavur, Tamil Nadu, India Smart Energy Informatics Laboratory (SEIL), Indian Institute of Technology-Bombay, India c Discrete Mathematics Research Laboratory (DMRL), Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu, India b
article
info
Article history: Received 16 March 2019 Received in revised form 20 September 2019 Accepted 27 September 2019 Available online 18 October 2019 Keywords: Cloud service provider selection MCDM QoS attributes Rank centroid Shannon entropy Trustworthy CSPs
a b s t r a c t Cloud service provider selection, an important Multi-Criteria Decision Making (MCDM) problem involves intrinsic relations among the multiple alternatives, attributes and decision experts for the selection of trustworthy Cloud Service Providers (CSPs). Due to uncertain and incomplete nature of the cloud service provider evaluation data, i.e., Quality of Service (QoS) and user feedbacks, the identification of suitable CSPs with accurate service ranking remains an open research challenge. To address the above-mentioned challenge, this work presents an Improved Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregate Sum and Product Assessment (IIVIFS-WASPAS) based cloud service provider selection approach for the identification of Trustworthy CSPs (TCSPs). The proposed CSP selection approach employs integrated objective and subjective weight assessment method and IVIFSWASPAS method to determine the importance of QoS attributes and to rank the TCSPs respectively. Further, a novel preference-attitudinal score and accuracy function of IIVIFS have been designed based on the decision maker’s attitude to rank the TCSPs. Case studies using Cloud Armor, a real-world trust feedback dataset demonstrates the accuracy, effectiveness, and feasibility of IIVIFS-WASPAS approach for CSP selection problem in terms of sensitivity analysis and Rank Reversal Phenomenon (RRP). © 2019 Published by Elsevier B.V.
1. Introduction Over the last few decades, rapid advancements in Information and Communication Technologies (ICT) have an enormous impact on the fifth utility computing - ‘Cloud Computing’ through the provision of data-intensive services and computational resources on a subscription basis [1] . The innate advantages of cloud computing have attracted various governmental, academic and business organizations to migrate their business solutions to cloud infrastructures to make their business processes agile with minimal cost and management effort [2]. However, the proliferation of a wide range of Cloud Service Providers (CSPs) offering functionally-equivalent services with different performance and cost makes the selection of an appropriate and Trustworthy Cloud Service Providers (TCSPs) an unsolved research challenge For example, Google Drive, Onedrive, Bitriz24, MyDrive, etc. provides Storage as a Service (StaaS) at different performance (QoS attributes: availability, response time, price, and so on), cost with varied importance on the QoS attributes (Criteria). Problem Statement and Context: ‘Cloud service provider selection’, a significant and interesting research problem due to the ∗ Corresponding author. E-mail address: [email protected] (Shankar Sriram V.S.). https://doi.org/10.1016/j.future.2019.09.053 0167-739X/© 2019 Published by Elsevier B.V.
existence of a wide range of CSPs (alternatives) and uncertain assessment data (objective and subjective). In general, the performance of the CSPs is well-reflected by the QoS attributes. A user-service QoS evaluation/performance matrix which contains QoS values or users’ feedback values over the QoS attributes forms the major data source for CSP evaluation. Moreover, trustworthiness is a quality metric that expresses the performance of the CSPs with respect to different QoS attributes. Several trustbased service selection approaches based on rough set theory [3– 7], evidence theory [8], probability theory [9,10], fuzzy set theory [11], etc., have been developed for the design of a robust cloud service selection model. CSP selection problem can be formulated as a Multi-Criteria Decision-Making (MCDM) problem due to the intrinsic relationship among the multiple QoS attributes, alternatives and decision makers’ opinions [12–22]. Recent research works based on Fuzzy based MCDM (FMCDM) approaches [23–25] like Intuitionistic Fuzzy Set (IFS) [26–29], Neutrosophic Fuzzy Set (NFS) [30], Hesitant Fuzzy Set (HFS) [31], etc., demonstrated their effectiveness in dealing with uncertain data and ambiguous decisions for cloud service provider selection. However, determining the trustworthiness of the service providers with respect to a set of user-specific QoS attributes is complex due to personal biases in the users’ preferences, imprecise weights of the QoS
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parameters, multi-dimensional evaluation process, vagueness in the decision-making process, and Rank Reversal Phenomenon (RRP) [32]. Solution and Novelty: To address the afore-mentioned issues in CSP selection, this work presents an Improved Interval-Valued Intuitionistic Fuzzy Set-Weighted Aggregate Sum and Product Assessment (IIVIFS-WASPAS) approach for the identification of TCSPs. IIVIFS-WASPAS employs (i) IVIFS — analyse the fuzziness of the user preferences, (ii) Integrated weight assessment method — identify the importance of QoS attributes through IVIFS-Shannon Entropy (SE) for objective weight assessment and Rank-centroid for subjective weight assessment and (iii) IVIFSWASPAS — rank the TCSPs. Further, a novel preference attitudinal score and accuracy function was developed to defuzzify the IVIFS value without loss of information. The major motive behind the application of IVIFS is that it can handle vague and imprecise trust feedback data (crisp data) by expressing satisfaction, dissatisfaction and uncertainty of the CSPs through membership degree/truthfulness, non-membership degree/falsity, and hesitant degree in the form of intervals. Further, WASPAS aggregates Weighted Sum Model (WSM) and Weighted Product Model (WPM) to enable high ranking accuracy in dynamic environment scenarios. In general, the crisp data has uncertainty since it is hard for the users to express their level of satisfaction/dissatisfaction on the cloud service providers with respect to the QoS attributes. Therefore, the conversion of crisp data into IVIFS enables the users to express their satisfaction, dissatisfaction & uncertainty and thereby enabling accurate cloud service ranking. Contributions: The major contributions of the IIVIFS-WASPAS are highlighted as follows: 1. An Improved Interval Valued Intuitionistic Fuzzy Set (IIVIFS) based cloud service provider selection approach is presented to identify the trustworthy CSPs. 2. Uncertainty in the assessment data is handled by converting the user feedbacks (crisp numbers) into IVIFS numbers since it reflects truthfulness, falsity and hesitancy of the CSPs with respect to the QoS attributes. 3. A novel integrated objective and subjective weight assessment approach is designed to determine the importance of the QoS attributes for accurate service ranking. 4. A novel preference attitudinal score and accuracy functions based WASPAS is designed for service ranking without loss of information. 5. The effectiveness of the IIVIFS-WASPAS was demonstrated with the case study using the sample dataset from the Cloud Armor trust feedback dataset in terms of sensitivity analysis and rank reversal phenomenon. The rest of the paper is organized as follows: Section 2 discusses the literature review about cloud service provider selection using different FMCDM approaches. Section 3 provides a detailed insight into the basics of IVIFS, score and accuracy functions of IVIFS. Section 4 presents a novel preference-attitudinal score and accuracy functions for ranking CSPs and working of the IIVIFS, the proposed cloud service provider selection approach. Section 5 presents the case study using Cloud Armor, a trust feedback dataset to analyse the efficiency and reliability of IIVIFS over the state-of-the-art IVIFS based cloud service provider selection approaches. Section 6 concludes the paper. 2. Literature review ‘Cloud service provider selection’ is modelled as a MCDM problem since the trustworthiness of the CSPs can be evaluated
based on: (i) discovering cloud service providers (Alternatives); (ii) identify QoS attributes (Criteria); (iii) assess the ratings of the CSPs’ and weights of the QoS attributes; (iv) aggregate the ratings of the CSPs and weights of the QoS attributes to compute the trustworthiness of each CSP across the QoS attributes, and (v) select the trustworthy CSP. Recent research studies on Fuzzy based MCDM (FMCDM) approaches has gained huge momentum over a wide range of MCDM based CSP selection approaches for the evaluation and identification of trustworthy CSPs [23]. Alam et al. [33] developed Fuzzy Analytic Hierarchy ProcessWASPAS (FAHP-WASPAS), an uncertainty-aware hybrid MCDM approach to evaluate and rank cloud services. FAHP-WASPAS employs FAHP to obtain relative weights of the primary & secondary attributes and WASPAS to rank the cloud services. The efficiency of FAHP-WASPAS was validated using a case study with six realworld public IaaS cloud services (S1, S2, S3, S4, S5, S6), nine main criteria (C1 − C9), and thirty sub-criteria (C 11 − C 13, C 21 − C 23, C 31 − C 33, C 41 − C 44, C 51 − C 53, C 61 − C 63, C 71 − C 74, C 81 − C 83, C 91 − C 94). Further, sensitivity analysis was conducted to verify the robustness of FAHP-WASPAS. Mohamed Abdel-Basset et al. [30] presented a Neutrosophic Multi-Criteria Decision Analysis (NMCDA) technique to estimate the quality of cloud services. The neutrosophic concept has been utilized to aggregate different opinions of the decision makers and improve their consistency rate. Analytic Hierarchy Process (AHP) was introduced in neutrosophic concept to handle ambiguous and inconsistent information presented in the procedure of cloud service estimation. The performance of NMCDA was evaluated using a case study of big e-learning service provider company in Egypt. It considered three cloud service alternatives (Dropbox, Google Drive, and Microsoft Sky Drive) and five criteria (Security, Performance, Accessibility, Scalability, and Adaptability) to select appropriate cloud service provider that provide safety and privacy to the company. Marija Paunovi et al. [34] proposed a two-stage Fuzzy Logic (2sFL) model based on FAHP and fuzzy logic approaches to evaluate cloud service suppliers. The fuzzy logic utilized in 2sFL model minimizes the subjectivity of the decision makers. 2sFL model consists of two stages: (i) The first stage represents the input parameters (estimate the relationship between experts expressed in fuzzy numbers) and output (total evaluation of the cloud suppliers) and (ii) Second stage utilizes the fuzzy logic and approximate reasoning to observe the variables and define them by fuzzy sets. A simulation experiment with three cloud service suppliers (CS1, CS2, CS3), three experts, and five technology perspective terms (criteria-performance, capability, service level, quality & security, and privacy) was carried out using MATLAB to validate the efficiency and rationality of 2sFL model. Aveek Basu and Sanchita Ghosh [35] applied Fuzzy based Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) technique to identify an appropriate cloud service provider and cloud type for an organization. The performance of FTOPSIS was assessed with three different experts (D1, D2, D3) to evaluate three types of cloud service providers (Amazon Web Services, IBM Bluemix, Google Compute Engine) over nine features (Business size support, Support for versatile industries, Control interface features, Availability of support services, Server OD types, Preconfigured operating systems, Available runtimes, Middleware, Native databases). Gülçin Büyüközkan et al. [36] proposed a novel Group Decision Making (GDM) based IVIF MCDM techniques for the Cloud Computing Technology Provider Selection (CCT PS). IVIF MCDM techniques such as Interval-Valued Intuitionistic Fuzzy AHP (IVIF AHP) (determine the weights of criteria and subcriteria), IVIF COmplex PRoportional ASsessment (IVIF COPRAS), IVIF multi-objective optimization by ratio analysis plus the full multiplicative form (IVIF
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
MULTIMOORA), and IVIF VišekriterijumskoKompromisnoRangiranje (IVIF VIKOR) rank the CCT providers based on the Decision Makers (DMs) evaluation of alternatives with respect to the criteria. The performance of GDM based IVIF MCDM techniques was evaluated using a case study of ABC Group with three DMs (Vicechancellor, Professor from the academy and IT Manager), six major criteria & 27 sub-criteria and four CCT providers (Amazon Cloud, Google Cloud, IBM Cloud and Azure Cloud) in terms of availability and flexibility. Rakesh Ranjan Kumar et al. [11] designed a novel cloud service selection model based on AHP and Fuzzy TOPSIS to rank cloud service providers. The overall process comprises of three major steps: (i) Identify evaluation criteria to select cloud service providers, (ii) Apply AHP to determine the importance of evaluation criteria, and (iii) Apply Fuzzy TOPSIS to rank cloud services. The efficiency and robustness of the AHP and Fuzzy TOPSIS model was validated using a sample dataset (six cloud database servers over ten criteria) obtained from Cloud Harmony reports and compared with state-of-the-art MCDM approaches like AHP and improved TOPSIS in terms of sensitivity analysis. Neda Tanoumand et al. [37] proposed FAHP technique which employs Fuzzy Extent Analysis (FEA) method to select the suitable cloud service provider for the demanding enterprise. FEA has been used to elicit weights of the criteria with respect to each cloud service provider (alternative) and FAHP choose the optimal cloud service provider for the enterprises. A pilot case study with five cloud service providers (Amazon, Windows, Google, Rackspace, and IBM) and six criteria (acquisition cost and transaction cost, availability, storage capacity, CPU, performance, and security) was used to assess the performance of FAHP technique. Sangwon Lee and Kwang-Kyu Seo [38] proposed a hybrid MCDM model that integrates Balanced Score Card (BSC), Fuzzy Delphi Method (FDM), and Fuzzy Analytical Hierarchy Process (FAHP) to select appropriate IaaS cloud services for organizations. The hybrid MCDM model employs BSC for the identification of the decision-making factors; FDM for the identification of the critical decision-making factors and FAHP to determine the weights of BSC criteria and sub decision-making factors. Further, FAHP was used to rank and select the best cloud service provider. The performance and efficiency of the hybrid MCDM cloud service selection model was evaluated using a case study with four BSC criteria (Financial, Customer, Internal business process, Learning and growth), fourteen decision-making factors and five cloud service providers. Further, the robustness of the proposed model was validated using sensitivity analysis under the consideration of diversified and numerous expert groups. Sun Le et al. [39] proposed a Cloud-Fuzzy User-oriented Cloud SeRvice Selection (Cloud-FuSeR) System to recommend top-K cloud services. The efficiency of Cloud-FuSeR was evaluated using a case study of cloud storage service selection based on two aspects, namely service function matching using Fuzzy LightWeight (FLW) similarity model and ranking cloud services using FTOPSIS method in terms of Mean Squared Error of Ranks (MSER), TOP rank matched count (TOP), Match count (MATCH), and variation between TOP and expected results of the TOPSIS method. Christian Esposito et al. [40] formulated fuzzy logic (express vagueness in the subjective preferences), fuzzy inference, Dempster–Shafer theory of evidence (service provider selection), and game theory (obtain trustworthy service providers by maximizing the user requirements satisfaction and minimizing the storage services price) for cloud storage service provider selection. Simulation on a testbed with 30 storage service providers and 4 QoS attributes was carried out using Objective Modular Network Testbed in C++ (OMNeT++) to validate the efficiency and quality of the presented cloud service selection model. Hua ma et al. [41] proposed Cloud service Interval Neutrosophic Set (CINS) based on Interval Neutrosophic Set (INS) and
93
time period features of cloud services to select the trustworthy cloud service providers. INS measure the uncertainty of cloud service providers and compare the candidate service providers with trade-off between performance-costs and potential risks through the cloud model. Further, entropy weight measure was defined to compute the weights of the time periods to compute the difference between the candidate service providers. The experiments were carried out using WS-DREAM #3, a real-world dataset to analyse the performance of CINS in terms of risk-sensitive and performance-cost-sensitive service selection modes. S.P. Wan and J. Xu [42] developed a novel Multi-Attribute Group Decision-Making (MAGDM) with Triangular Intuitionistic Fuzzy Numbers (TIFNs) to evaluate and select the trustworthy services. The TIFNs consider the risk preference of DMs and their weights are determined based on the similarity between the individual and the average decision. The efficiency of MAGDM with TIFNs was validated using a case study of online supplier selection with three DMs, five trust factors (product quality (a1 ), service attitude (a2 ), technology security (a3 ), website design embodies appearance & ease use (a4 ), and shipping speed (a5 )) and three sellers Handuyishe (S1 ), Niman (S1 ) and Liebo (S3 ). Santoso Wibowo et al. [23] presented a fuzzy Multi-Criteria Group Decision Making (MCGDM) method that employs TOPSIS and the Choquet integral operator to evaluate the performance of cloud services in an uncertain environment. The efficiency of fuzzy MCGDM method was validated using a case study of Company A, an e-learning service provider with four cloud service alternatives (iCloud (A1 ), hiCloud (A2 ), Cloud drive (A3 ) and SmartCLOUD (A4 )), three DMs and five criteria (security (C1 ), performance (C2 ), service accessibility and usability (C3 ), scalability (C4 ) and adaptability (C4 )). Jingyi Bo et al. [43] proposed a new Multiple Attribute Decision Making (MADM) method with intuitionistic fuzzy information to assess the performance of cloud computing service evaluation system. The applicability and availability of the proposed model was verified using four alternatives (A1 , A2 , A3 and A4 ) on five attributes (security & risk (C1 ), data (C2 ), services (C3 ), resources (C4 ) and economic dimensions (C5 )). Thiruselvan Subramanian and Nickolas Savarimuthu [24] proposed a CloudSelect framework for cloud service evaluation and selection satisfying consumer’s requirements in cloud marketplace. The CloudSelect includes Fuzzy Analytic Network Process (FANP) to determine the relative weight of criteria and fuzzy TOPSIS, fuzzy Elimination and Choice Translating Reality (ELECTRE) to evaluate and rank the cloud services. The efficiency and robustness of the CloudSelect framework was validated using a case study on multimedia company with six collaboration tool providers (A1 , A2 , A3 , A4 , A5 and A6 ) over six criteria and compared with state-of-the-art MCDM approaches like SMICloud and MCISS in terms of computational complexity and sensitivity analysis. Gai-Li Xu et al. [44] developed a novel MAGDM with IVIFSs for cloud service selection. The decision experts’ preference values are expressed in the form of IVIFSs since it is flexible to measure the qualitative attributes than the crisp numbers. The extended Grey Relational Analysis (GRA) and multi-objective programming model used to determine the weights of decision experts and attributes. Further, the score and accuracy function has been used to rank the cloud services. The efficiency of the presented model was illustrated with an example of four experts (e1 , e2 , e3 and e4 ), four cloud services (SAP Sales on Demand (A1 ), Salesforce Sales Cloud (A2 ), Microsoft Dynamic CRM (A3 ) and Oracle Cloud CRM (A4 )) over five attributes (performance (u1), payment (u2), reputation (u3), scalability (u4 and security (u5)). Wenjuan Fan et al. [45] developed a novel hybrid two-stage model that employs fuzzy gap evaluation model (first stage) and
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
an Evidence Reasoning (ER) approach (second stage) for Cloud service Trustworthiness Evaluation (CTE). The first stage identifies the gap between the importance and performance criteria to evaluate the quality of cloud service providers. The second stage based on the belief structure performs robust decision making by analysing CTE from different perspectives. The performance of the hybrid model was analysed using a case study on public storage services and business management services provided by Nirvanix and BMC software in terms of Performance-Importance (P-I), Delivery-Importance (D-I), and Performance-Delivery (P-D) perspectives of cloud service users and cloud service providers. Chen-Tung Chen et al. [46] proposed a decision-making model that integrates fuzzy AHP with Interval-Valued Fuzzy Set (IVFS) to determine the fuzzy weights of criterion. Further, 2-tuple linguistic variables express the performance rating of the cloud service providers (alternatives) and obtain the ranking of cloud service providers. A case study with three cloud computing suppliers (A1 , A2 , A3 ), three decision-makers (p1 , p2 , p3 ) and 9 sub-criteria (C11 , C12 , C13 , C21 , C22 , C23 , C31 , C32 , C33 ) was used to assess the performance of the presented decision-making model. The above-mentioned variants of FMCDM approaches employs different factors and techniques for the identification of TCSPs. However, these methods do not address vagueness and uncertainty in the evaluation data and Rank Reversal Phenomenon (RRP) since they consider only the user’s satisfaction and dissatisfaction with respect to the QoS attributes rather than user uncertainty. Therefore, this research work presents an Improved Interval Valued Intuitionistic Fuzzy Sets (IIVIFSs) based cloud service selection approach which employs IVIFS, integrated weight assessment method, preference attitudinal based score and accuracy function and WASPAS to address the existing challenges in the CSP selection problem. 3. Materials and methods
Interval-Valued Intuitionistic Fuzzy Set (IVIFS) formulated by Atanassov and Gargov is defined in terms of interval numbers rather than crisp numbers to express the Membership Degree Function (MDF) and the Non-Membership Degree Function (NMDF) [47]. Further, the Hesitancy Degree Function (HDF) is defined using MDF and NMDF. Definition 3.1 ([48]). Let ϓ be the universe of discourse and ß is ´ ) in ϓ is defined as in Eq. (1). any element in ϓ, then IFS (υ ß, fυ´ (ß) , ῆυ´ (ß) |ß ∈ ϓ
{⟨
⟩
}
(1)
where, fυ´ (ß) and ῆυ´ (ß) is the MDF and the NMDF of υ´ , respectively. For each point in ß, where ß ∈ϓ, fυ´ (ß) , ῆυ´ (ß) ∈ [0, 1] and 0 ≤ fυ´ (ß) + ῆυ´ (ß) ≤ 1. For each IFS (υ´ ) in ß, let þ (ß) = 1 − fυ´ (ß) − ῆυ´ (ß) be the indeterminacy degree or hesitancy degree (uncertainty degree) function of the element ß to the set υ´ [48,49], where 0 ≤ þ (ß) ≤ 1, ∀ ß ∈ ϓ. For a given element ß, the pair fυ´ (ß) , ῆυ´ (ß) is defined as an Intuitionistic Fuzzy (IFN) [50]. Without the loss of ( Number ) generality, use ζ = fζ , ῆζ to represent IFN that satisfies fζ ∈ [0, 1] , ῆζ ∈ [0, 1] and 0 ≤ fζ + ῆζ ≤ 1.
(
)
Definition 3.2 ([51]). Suppose ϓ is a universe of discourse and ß is any element in ϓ, then IVIFS (Ʋ) in ϓ is defined as in Eq. (2).
Ʋ=
ß, ƑƲ (ß) , ȠƲ (ß) |ß ∈ ϓ
{⟨
⟩
}
þƲ (ß) = 1 − ƑƲ (ß) − ȠƲ (ß) = HƲ (ß)+ , HƲ (ß)−
[
]
] [ = 1 − ΨƲ (ß)− − NƲ (ß)− , 1 − ΨƲ (ß)+ − NƲ (ß)+
(2)
where, ƑƲ (ß) : ϓ → Γ ([0, 1]) and ȠƲ (ß) : ϓ → Γ ([0, 1]); Γ ([0, 1]) represents the set of all closed sub intervals of [0, 1].
(3)
Therefore, the Interval-Valued Intuitionistic Fuzzy Value (IVIFV) or Interval-Valued Intuitionistic Fuzzy Number (IVIFN) ] ([ or IVIFS (Ɽ) can be represented as Ɽ = ΨƲ (ß)+ , ΨƲ (ß)− ,
] ([ − + = ]) ΨƲ (ß) , ΨƲ (ß) , [ or Ɽ ] NƲ (ß)+ , NƲ (ß)− , HƲ (ß)+ , HƲ (ß)− . NƲ (ß)+ , NƲ (ß)−
[
])
[
Definition 3.3 ([51]). If Ẋ, Ẏ ∈ IVIFS (ϓ), then the subset relation is represented as Ẋ ⊂ Ẏ, if and only if ΨẊ (ß)+ ≤ ΨẎ (ß)+ , ΨẊ (ß)− ≤ ΨẎ (ß)− and NẊ (ß)+ ≥ NẎ (ß)+ , NẊ (ß)− ≥ NẎ (ß)− , ∀ ß ∈ ϓ. Definition 3.4 ([51]). The complement (Ɽc ) of IVIFS Ɽ = [ƑƲ (ß), ȠƲ (ß), þƲ (ß)] is defined by (Ɽc ) = [ȠƲ (ß), ƑƲ (ß), þƲ (ß)]. Definition 3.5 ([52]). The Schweizer-Sklar (SS) operations involve SS-Sum, SS-Difference (subtraction), SS-Product, and SS-Division. The SS-Difference and SS-Division are derived based on the additive inverse and multiplicative inverse of SS-Sum and SS-Product (Special cases of Archimedean t-norm and t-conorm (ATT)). − − + − + − and Q = Ƒ+ Let P = Ƒ+ Q , ƑQ , ӃQ , ӃQ P , ƑP , ӃP , ӃP be the two IVIFS, then the relation among MDF, NMDF and SS operational rules (γ < 0) of IVIFS are defined as in Eqs. (4)–(8).
] [
([
])
] [
([
+ − − + + − − P ≤ Q ⇔ Ƒ+ P ≤ ƑQ , ƑP ≤ ƑQ , ӃP ≤ ӃQ , ӃP ≤ ӃQ
3.1. Interval-Valued Intuitionistic Fuzzy Set (IVIFS)
υ´ =
For our convenience, ) and upper el( ) we (represent the lower ements of MDF ƑƲ (ß) as( ΨƲ ()ß)+ ,(ΨƲ (ß)− and lower ) and upper elements of NMDF ȠƲ (ß) as NƲ (ß)+ , NƲ (ß)− , such that 0 ≤ ΨƲ (ß)− + NƲ (ß)− ≤ 1, ΨƲ (ß)+ , NƲ (ß)+ ≥ 0, ∀ ß ∈ ϓ. For each element ß ∈ ϓ, the interval-valued Hesitancy Degree (HD) of Ʋ is defined as in Eq. (3).
([
) + γ
) γ1
) + γ
(4)
]
+ 1 − ƑQ − 1 , , ) γ1 ( )γ − 1 1 − 1 − ƑP + 1 − Ƒ− Q [ ( ) γ1 ]) +γ +γ ӃP + ӃQ − 1 , ( −γ ) γ1 γ ӃP + Ӄ− Q −1 ([ ) ) γ1 ] )γ ( (( + γ − 1 + 1 + Ƒ 1 − 1 − Ƒ+ , P Q P⊖Q= , ( ) ) γ1 (( ) − γ − γ 1 − 1 − ƑP + 1 + ƑQ − 1 [ ( ) γ1 ]) γ +γ Ӄ+ , P − ӃQ − 1 ) γ1 ( −γ γ ӃP − Ӄ− − 1 Q ([ ( ) γ1 ] γ +γ ƑP + Ƒ+ − 1 , Q P⊗Q= , ( −γ ) γ1 −γ ƑP + ƑQ − 1 [ (( )γ ( )γ ) 1 ]) 1 − 1 − Ӄ+ + 1 − Ӄ+ −1 γ , P Q (( )γ ( )γ )1 1 − 1 − Ӄ− + 1 − Ӄ− −1 γ P Q ⎛⎡ ( γ γ ⎤ 1 + +γ ) γ Ƒ+ P ƑQ +1−ƑQ , + ⎜⎢ ⎥ ƑQ P ⊘ Q = ⎝⎣ ( ⎦, 1 −γ −γ −γ ) P⊕Q=
1−
((
1 − ƑP
((
) − γ
ƑP ƑQ +1−ƑQ Ƒ− Q
⎡
(
Ӄ− P
γ
(
1−Ӄ+ P
(
])
(6)
(7)
γ
)γ ( )γ γ + Ӄ− − Ӄ− P −1 P
) γ1
⎢ 1− , ⎢ Ӄ− P ⎢ ⎢ ( ) γ1 ( )γ ( )γ ⎢ γ γ Ӄ− 1−Ӄ+ + Ӄ− −Ӄ− ⎣ Q Q Q −1 Q 1− Ӄ− P
(5)
⎤⎞ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎦⎠
(8)
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
In this work, the SS operational laws are used for cloud service selection due to the presence of variable parameter (γ ; γ < 0) that is superior to the basic IVIFS operations and provides flexibility [53]. To compare two IVIFS and rank the IVIFS, we review the existing score and accuracy functions. Definition 3.6 ([54]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS (0 ≤ Ƒ+ ≤ Ƒ− ≤ 1, 0 ≤ Ӄ+ ≤ Ӄ− ≤ 1, and 0 ≤ Ƒ− + Ӄ− ≤ 1), the score function (S) of an IVIFS (J) can be represented as in Eq. (9).
([
] [
])
Ƒ+ − Ӄ+ + Ƒ− − Ӄ−
(9) , ∀ SXu (J) ∈ [−1, 1] 2 The larger the score value of the IVIFS (SXu (J)), the larger the IVIFS (J). Suppose, if any two IVIFS are equal, then the accuracy function is required to measure the accuracy of MDF and NMDF of IVIFS. SXC (J) =
Definition 3.7 ([54]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS (0 ≤ Ƒ+ ≤ Ƒ− ≤ 1, 0 ≤ Ӄ+ ≤ Ӄ− ≤ 1, and 0 ≤ Ƒ− + Ӄ− ≤ 1), the accuracy function (A) of an IVIFS (J) is defined as in Eq. (10).
] [
([
])
Ƒ+ + Ƒ− + Ӄ+ + Ӄ−
, ∀ AXC (J) ∈ [0, 1] (10) 2 The larger the accuracy value of IVIFS (AXC (J)), the larger the IVIFS (J).
AXC =
Definition 3.8 ([55]). Let J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− be an IVIFS, a novel accuracy function (N) of an IVIFS (J) is defined as in Eq. (11).
([
+
Ӄ +Ӄ
] [
])
−
, ∀ NYe (J) ∈ [−1, 1] (11) 2 Ye et al. [55] formulated a different expression to measure the accuracy degree of an IVIFS (Eq. (9)). The higher the accuracy value (NYe (J)), the greater the degree of accuracy of IVIFS (J).
NYe (J) = Ƒ+ + Ƒ− − 1 +
Definition 3.9 A ]) novel accuracy function (Ԓ) of an IVIFS, ] ([56]). [ ([ J = Ƒ+ , Ƒ− , Ӄ+ , Ӄ− can be computed as in Eq. (12).
ԒLS (J) =
( ) ( ) Ƒ+ + Ƒ− − Ӄ− 1 − Ƒ− − Ӄ+ 1 − Ƒ+ 2
,
∀ ԒLS (J) ∈ [−1, 1]
(12)
The larger the accuracy value of IVIFS (ԒLS (J)), the greater the IVIFS (J).
([ ] [ + − ]) − Definition[ 3.10 ([57]). Let J =[ Ƒ+ , Ƒ , Ӄ ,Ӄ be an IVIFS, ] ] such that Ƒ+ , Ƒ− ⊆ [0, 1] , Ӄ+ , Ӄ− ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the score function (ϑ) of an IVIFS (J) defined by Wang and Chen is given in Eq. (13).
ϑWC (J)
Ƒ+ + Ƒ− +
√ − −( ) √ ( ) Ƒ Ӄ 1 − Ƒ+ − Ӄ+ + Ƒ+ Ӄ+ 1 − Ƒ− − Ӄ−
=
2
∀ ϑWC (J) ∈ [0, 1]
,
(13)
The larger the score value of IVIFS (ϑWC (J)), the higher the IVIFS (J). − + − Definition[ 3.11 ([58]). Let J =[ Ƒ+ , Ƒ be an IVIFS, ] ] , Ӄ ,Ӄ such that Ƒ+ , Ƒ− ⊆ [0, 1] , Ӄ+ , Ӄ− ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the score function (S) of an IVIFS (J) is represented in Eq. (14).
([
SNWC (J) =
] [
])
( + )( ) ( )( ) Ƒ + Ƒ− Ƒ+ + Ӄ+ − Ӄ+ + Ӄ− Ƒ− + Ӄ− 2
,
95
∀ SNWC (J) ∈ [−1, 1]
(14)
The larger the score value of IVIFS(SNWC (J)), the higher the degree of score of the IVIFS (J). − + − Definition[ 3.12 ([58]). Let J =[ Ƒ+ , Ƒ be an IVIFS, ] ] , Ӄ ,Ӄ + − + − such that Ƒ , Ƒ ⊆ ([0,)1] , Ӄ , Ӄ ⊆ [0, 1] and Ƒ− + Ӄ− ≤ 1, the accuracy function Ӑ of an IVIFS (J) is defined as in Eq. (15).
([
ӐNWC (J) ( =
1 − Ƒ+ + Ƒ−
)(
] [
])
1 − Ƒ+ − Ӄ+ + 1 − Ӄ+ + Ӄ−
)
(
)(
1 − Ƒ− − Ӄ−
2
∀ ӐNWC (J) ∈ [0, 1]
) ,
(15)
) ( The larger the accuracy value of IVIFS ӐNWC (J) , the higher the degree of accuracy of the IVIFS (J). + − + − Definition ([ + − ] 3.13 [ + ([54]). ]) If P = ƑP , ƑP , ӃP , ӃP and Q = − ƑQ , ƑQ , ӃQ , ӃQ are two IVIFS, then the following constraints should satisfy the score function (S) and the accuracy function (A) of IVIFS.
([
] [
])
(1) If S (P) > S (Q), then P > Q. (2) If S (P) = S (Q), then consider the conditions listed below:
• If A(P) > A(Q), then P > Q. • If A (P) = A(Q), then P = Q. Where, S (P) and S (Q) represent the score functions of IVIFS. Similarly, A (P) and A(Q) indicates the accuracy functions of IVIFS. Different score and accuracy functions of IVIFS (Eqs. (9)–(15)) provide better ranking of the alternatives. However, there exists inaccuracy in ranking when the sum of lower bound of the membership degrees and the sum of the upper bound of non-membership degrees are equal. Further, Eqs. (9)–(15) does not fully utilize the IVIFS information (MDF, NMDF, and HDF) and therefore leads to imprecise ranking. To address the same, we present a novel preference-attitudinal score and accuracy functions using hesitancy degree for ranking IVIFS (Section 4.1). 4. Improved Interval-Valued Intuitionistic Fuzzy Set: Proposed cloud service provider selection approach 4.1. An improved score and accuracy function of IVIFS based on the preference attitude of assessor/decision maker/user IIVIFS, the proposed cloud service provider selection approach evaluates the cloud service providers based on the aggregated IVIFS. Therefore, it is necessary to find out the ways to compare two IVIFS for accurate service ranking. There exists several score and accuracy functions to compare two IVIFS, however they fail to identify the exact difference between two IVIFS. To address the above-mentioned challenge, we present a novel preference attitudinal based accuracy and score function with an attitudinal parameter in double integral for IVIFN. The proposed accuracy and score function is the extension of Jian Lin et al. work on preference attitudinal accuracy and score functions of IFN [59]. 4.1.1. The preference attitudinal accuracy function Definition 4.1. Let δ = feasible domain of {
U+ , U− , N+ , N− be an IVIFN. The IVIFN (δ) }is defined as FDδ ( + + H+ ; U− ≤X≤U− +H− ) = (X, Ү) NU+ ≤≤ҮX≤≤NU+ + where, H+ = 1 − U− − + +H ; N− ≤Ү≤N− +H−
([
] [
])
N− and H− = 1 − U+ − N+ . By considering the hesitancy degree of δ , the feasible domain (FDδ )indicates the set of feasible interval-valued intuitionistic fuzzy numbers with respect to δ .
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Definition 4.2. Let δ = U+ , U− , N+ , N− , H+ , H− be an IVIFN. The preference attitudinal accuracy function of δ is given in Eq. (16).
([
Aρ (δ) =
∫∫
1 area (FDδ )
] [
] [
])
(ρ X + (1 − ρ) Ү) dXdҮ
(16)
FDδ
Where, FDδ and area (FDδ ) represent the feasible domain of IVIFN and the area of feasible domain (FDδ ) respectively. The parameter ρ (ρ ∈ [0, 1]) indicates the assessor’s (or user’s) preference attitude or the level of decision maker towards the positive, negative, and neutral information, i.e., ρ = 0.5 specifies the assessor or decision maker is neutral to the positive and negative information. average value of accuracy The term Aρ (δ) represents the ∫∫ function over FDδ . The integral part FD (ρ X + (1 − ρ) Y) dXdY δ is equal to the volume of the triangular prism O1 . It means that Aρ (δ) can be considered as an average height of oblique triangular prism O1 . From Definition 4.1, we define the area of feasible domain (FDδ ) (Eq. (17)). 1
)2 1 ( + − )2 1 (( area (FDδ ) = H = H ,H = 1 − U− − N− , 2 2 )2 2
) + 2
+
(
1−U −N
(17)
(ρ X − (1 − ρ) Y) dXdY (∫ ∫ + −
FDδ
,1−N
]
)
1−X
(ρ X − (1 − ρ) Y) dY dX [N+ ,N− ] [U+ ,U− ] )2 1( = 1 − U+ − U− − N+ − N− 6( ) ) ( × U+ + U− − 2 N+ + N− − 1
=
+
ρ(
1 − U+ − U− − N+ − N−
)2
(6 ) × U+ + U− + N+ + N− + 2
(22)
Based on Eqs. (17) and (22), the preference attitudinal score function of IVIFS is defined in Eq. (23). Sρ (δ) =
)
U+ + U− − 2 N+ + N− − 1
ρ( 3
3 +
U + U + N+ + N− + 2
(
Sρ (δ) = ρ
)
X
(ρ X + (1 − ρ) Y) dX dY
=
[U+ ,U− ] [N+ ,N− ] )2 1( 1 − U+ + U− − N+ − N− = 6( ( )) × 1 − U+ + U− + 2 N+ + N−
ρ(
1 − U+ + U− − N+ − N−
2
]
−
)
(23)
Eq. (23) can be rewritten as in Eq. (24).
(ρ X + (1 − ρ) Y) dXdY (∫ ∫ + − [1−N
,1−N
[1−N
+
FDδ
+
∫∫
(
Since,
∫∫
Where, FDδ indicates the feasible domain of IVIFN (δ) and Sρ (δ) is the average score function over FDδ . If the term ϑup indicates the volume of P2 and ϑbelow is the volume of P3 , then ∫∫ (ρ X − (1 − ρ) Ү) dXdҮ = ϑup − ϑbelow . Accordingly, Sρ (δ) FDδ can be considered as the average values of variable T over FDδ . Since,
+ (1 − ρ)
)2 (
U+ − U− − N+ − N−
)
)
2 U+ + U− − N+ − N− + 1 3 ( ) U+ + U− − 2 N+ + N− − 1 3
(24)
In Eqs. (20) and (24), integer 1 (assumption H+ + H− = 1) is replaced with hesitancy degree to utilize full IVIFS information, i.e., MDF, NMDF, and HDF to obtain the ranking without loss of information.
(18) Therefore, the preference attitudinal accuracy function is defined in Eq. (19).
(
Aρ (δ) =
1 − U+ + U− + 2 N+ + N−
)
3 ( ) + ρ U+ + U− − N+ − N−
(19)
Eq. (19) can also be written as in Eq. (20).
)
(
Aρ (δ) = ρ
2 U+ + U− − N+ − N− + 1
+ (1 − ρ)
3 ) ( 2 N+ + N− − U+ − U− + 1
(20)
3
Since the user’s/decision maker’s attitude is dynamic, it is difficult to determine the exact or precise value of parameter (ρ). To address this issue, we consider the preference attitude of user towards the information to estimate the appropriate value of parameter (ρ). Table 1 presents the user’s attitude towards the information with the corresponding value of the parameter (ρ). 4.1.2. The preference attitudinal score function Definition 4.3. Let δ = U+ , U− , N+ , N(− be) an IVIFN. The preference attitudinal score function of δ Sρ (δ) is defined in Eq. (21).
([
Sρ (δ) =
1 area (FDδ )
∫∫ FDδ
] [
])
(ρ X − (1 − ρ) Ү) dXdҮ
(21)
4.2. IIVIFS-WASPAS: Working In this work, we present an Improved version of IntervalValued Intuitionistic Fuzzy Set-Weighted Aggregated Sum and Product Assessment (IIVIFS-WASPAS), which integrates a hybrid weight assessment model and IVIFS-WASPAS for the identification of TCSPs. IIVIFS-WASPAS addresses the uncertainty in the assessment data by converting the crisp data into IVIFS through expressing the MDF and NMDF in terms of intervals rather than precise numbers. Fig. 1 presents the workflow of IIVIFS-WASPAS, the proposed cloud service selection approach. The working of IIVIFS involves three phases: (i) Determine the performance of CSPs — The performance ratings of CSPs (Alternatives) for each QoS attributes are expressed in IVIFS/IVIFNs, (ii) Compute the weights of the QoS attributes — Assess the information about the importance of QoS attributes through the integrating the subjective and objective weights and (iii) Obtain the ranking order of CSPs — Rank CSPs and identify the TCSPs. 4.2.1. Phase 1: Determine the performance of CSPs with respect to the QoS attributes ( Consider a cloud service selection) problem with k CSPs Ṗi = {S1 , S2 , . . . , Sk } , ∀ i = 1, 2, . . . , k , which are assessed on ( the basis of l QoS attributes (QoS attributes) Ṡj = {C1 , C2 , . . . , Cl } , ∀j = 1, 2, . . . , l). The first phase of IIVIFS focuses on the evaluation of different QoS attributes (Criteria) and CSPs (Alternatives) for the identification of TCSPs. In simpler terms, the major objective of the first phase is to assess the performance of a multitude
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
97
Table 1 User’s preference attitude towards information and their corresponding values [59]. S.no.
Decision maker’s preference attitude
Parameter (ρ) value
1.
The negative information is absolutely preferred (NAP)
0
2.
The negative information is extremely preferred (NEP)
0.1
3.
The negative information is strongly preferred (NSP)
0.2
4.
The negative information is moderately preferred (NMP)
0.3
5.
The negative information is slightly preferred (NSP)
0.4
6.
The decision maker is neutral to the positive and negative information (NPN)
0.5
7.
The positive information is slightly preferred (PSP)
0.6
8.
The positive information is moderately preferred (PMP)
0.7
9.
The positive information is strongly preferred (PSP)
0.8
10.
The positive information is extremely preferred (PEP)
0.9
11.
The positive information is absolutely preferred (PAP)
1
Table 2 Conversion of crisp values into IVIFS [60]. Normalized crisp numbers (CN )
IVIFS
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
([0.065, 0.165] , [0.815, 0.835]) ([0.155, 0.255] , [0.725, 0.745]) ([0.245, 0.345] , [0.635, 0.655]) ([0.335, 0.435] , [0.545, 0.565]) ([0.425, 0.525] , [0.455, 0.475]) ([0.515, 0.615] , [0.365, 0.385]) ([0.605, 0.705] , [0.275, 0.295]) ([0.695, 0.795] , [0.185, 0.205]) ([0.785, 0.885] , [0.095, 0.115]) ([0.875, 0.975] , [0.005, 0.025])
of CSPs (Level-3) with respect to the several QoS attributes (Level 2) for the identification of TCSPs (Level 1-Goal) ( ) (Fig. 2). The performance ( ) matrix of each CSP Ṗi with respect to the QoS attributes Ṡj is expressed in IVIFS and an IVIFS performance matrix is constructed as detailed below: Step-1.1: Conversion of crisp data into IVIFS. In general, the cloud consumers express their preferences (feedbacks) for the quantitative attributes of the CSPs in terms of crisp values. This often leads to poor evaluation, loss of information, and less ranking accuracy. To overcome the challenges related to fuzziness and uncertainty in the data, we convert the crisp values to IVIFS (Algorithm 1). The quantitative attributes expressed ([ in the form ]) ] [ of crisp − . numbers are converted into IVIFN, Rij = Fij+ , Fij− , L+ ij , Lij [ + −] [ + −] The intervals Fij , Fij and Lij , Lij represent the MDF (degree of satisfaction) and NMDF (degree of dissatisfaction) of [ the CSPs ] (Ṗi ) on the quantitative attribute (Ṡj ), which satisfies Fij+ , Fij− ∈ [ ] − [0, 1] , L+ ∈ [0, 1] and Fij− + L− ij , Lij ij ≤ 1. Table 2 presents the conversion of crisp numbers to their corresponding IVIFS. Step-1.2: Formulate the IVIFS performance matrix with a set of CSPs (CSP 1 , CSP 2 , . . . , CSP m ) and QoS attributes ((A1 , A2), . . . , A(n ). ) Construct the IVIFS performance matrix IVIFSij k⤫l = Ƿij k⤫l , i = 1, 2, . . . , k; j = 1, 2, . . . , l with k CSPs ( ) and l QoS attributes. The IVIFS performance matrix IVIFSij k⤫l represents the performance index of ith cloud service provider to the jth attribute as defined in (Eq. (25)).
( The ) performance index of each CSP w.r.t each QoS attribute Ƿij is normalized in the range of [0,1] and then converted into respective IVIFS representation. Step-1.3: Normalize the IVIFS performance matrix. Normalization forms the integral and most important step in the evaluation of CSPs for effective decision making. It reduces the impact of high valued heterogeneous QoS attributes by transforming them in the range of [0,1]. The QoS attributes are assumed as benefit attributes ) ) an accurate ranking. The IVIFS perfor(( to obtain mance matrix IVIFSij k⤫l is normalized to balance the physical dimensions of the preference indices with respect to the various (( ) QoS attributes. ( ) ) The normalized IVIFS performance matrix ˜ ij ˜ R = Ƞ is computed using Eq. (26). k⤫l k⤫l
(
˜ ij Ƞ
)
=
([
k⤫l
] [
] [
+ ˜ − + ˜ − ˜ ˜+ ˜− ˜ U ij , Uij , Nij , Nij , Hij , Hij
+ ˜ where, U ij
])
(26) k⤫l
U+ ij
=
√
((
∑m
i =1
U+ ij
)2 ( )2 ) ; ∀ i + U− ij U− ij
− ˜ √ j = 1, 2, . . . , l; U ij =
∑m
((
∑m
((
U+ ij
i=1
)2 ( )2 ) ; ∀ i + U− ij
N+ ij
˜+ = √ j = 1, 2, . . . , l; N ij
N+ ij
i=1
N− ij
˜− = √ j = 1, 2, . . . , l; N ij ∑m
i=1
((
N+ ij
)2 ( )2 ) ; ∀ i + N− ij
)2 ( )2 ) ; ∀ i + N− ij
1, 2, . . . , k;
=
= 1, 2, . . . , k; = 1, 2, . . . , k;
= 1, 2, . . . , k; j =
− ˜+ = 1 − U ˜ ˜− 1, 2, . . . , l; H ij ij − Nij ; ∀ i = 1, 2, . . . , k; j = 1, 2, . . . , l;
˜ =1−U ˜−N ˜ ; ∀ i = 1, 2, . . . , k; j = 1, 2, . . . , l H ij ij ij −
+
+
4.2.2. Phase 2-compute weights for each QoS attributes The procedure to determine the weights of the QoS attributes is a significant method since it only has an impact on the CSPs ranking obtained by any MCDM method. The effectiveness of the proposed approach mainly depends on the defined set of QoS attributes through which the evaluation and selection of the CSPs are conducted. The proposed approach employs the integrated objective and subjective weight assessment approach
98
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Fig. 1. IIVIFS-WASPAS framework for cloud service provider selection.
Fig. 2. Hierarchical structure of cloud service provider selection.
to obtain the optimal weights of the QoS attributes. For the same, an improved version of Interval-Valued Intuitionistic Fuzzy Set-Shannon Entropy (IVIFS-SE), an objective weight assessment approach was designed to determine the objective weights of the
QoS attributes. The major motive behind the application of IVIFSSE is that the inclusion of hesitancy degree refines the arithmetic mean and acts as a better representative of the QoS attributes.
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
(
)
( )
IVIFSij k⤫l = Ƿij k⤫l =
⎛
− + − + − U+ ij , Uij , Nij , Nij , Hij , Hij
([
] [
] [
A1
]) k⤫l
A2
⎛ [ ] ⎞ ⎜ ⎜ T+ , T− , ⎜ ⎝ [ 11 11 ] ⎠ ⎜ + − ⎜ L11 , L11 ⎜ ⎜ ⎛ [ ] ⎞ ⎜ + − ⎜ T21 , T21 , ⎜ ⎝ ⎜ [ + ] ⎠ − ⎜ L21 , L21 ⎜ ⎜ . ⎜ . ⎜ . ⎜ ⎛ [ ⎜ ] ⎞ + − ⎜ T , =⎜ i1 Ti1 , ⎝ [ ⎜ ] ⎠ ⎜ + − ⎜ Li1 , Li1 ⎜ ⎜ . ⎜ . ⎜ . ⎜ ⎛ [ ] ⎞ ⎜ + ⎜ T(k−1)1 , T− (k−1)1 , ⎜ ⎝ ⎜ [ + ] ⎠ − ⎜ L(k−1)1 , L(k−1)1 ⎜ ⎜ ⎛ [ ] ⎞ ⎜ ⎜ T+ , T− , ⎝ ⎝ [ k1 k1 ] ⎠ + − Lk1 , Lk1
⎛ [ ⎝ [
T+ 12 , T12 ,
⎞
⎛ [ ···
] ⎠ −
+
T22 , T22 , +
−
]
⎞ ···
] ⎠ −
+
. . .
⎝ [
..
T+ i2 , Ti2 ,
] −
··· ..
]
⎞
L(k−1)2 , L(k−1)2
] ⎠
− T+ (k−1)2 , T(k−1)2 , +
−
⎛ [
]
⎝ [
− T+ k2 , Tk2 ,
⎝ [
···
⎞
T+ ij , Tij ,
···
···
Lij , Lij
..
]
⎞
L(k−1)j , L(k−1)j
] ⎠
− T+ (k−1)j , T(k−1)j ,
···
+
−
⎛ [
]
⎝ [
− T+ kj , Tkj ,
Lkj , Lkj +
+
−
]
⎞
Li(l−1) , Li(l−1)
] ⎠
Ti(l−1) , Ti(l−1) ,
⎝ [
+
−
+
−
⎝ [
]
⎞
Li(k−1) , Li(l−1)
] ⎠
− T+ i(k−1) , Ti(l−1) , +
−
]
⎞
L(k−1)(l−1) , L(k−1)(l−1)
] ⎠
− T+ (k−1)(l−1) , T(k−1)(l−1) ,
⎝ [
+
⎛ [ ···
⎝ [
−
]
⎞
Lk(l−1) , Lk(l−1)
] ⎠
− T+ k(l−1) , Tk(l−1) , +
−
T+ 1l , T1l ,
] −
⎞
⎟ ⎟ ⎟ ⎟ + ⎟ L1l , L1l ⎟ ⎟ ⎛ [ ⎞ ] ⎟ + − ⎟ T2l , T2l , ⎟ ⎝ [ ⎠ ⎟ ] + − ⎟ L2l , L2l ⎟ ⎟ . ⎟ . ⎟ . ⎟ ⎞ ⎛ [ ⎟ ] − ⎟ , , T T+ ⎟ il il ⎠ ⎝ [ ⎟ ] ⎟ + − ⎟ Lil , Lil ⎟ ⎟ . ⎟ . ⎟ . ⎛ [ ⎞ ⎟ ] ⎟ + − ⎟ T(k−1)l , T(k−1)l , ⎟ ⎝ [ ] ⎠ ⎟ + − ⎟ L(k−1)l , L(k−1)l ⎟ ⎟ ⎛ [ ] ⎞ ⎟ + − ⎟ Tkl , Tkl , ⎠ ⎝ [ ⎠ ] + − Lkl , Lkl ⎝ [
. . .
⎛ [ ···
⎛ [
. . .
.
⎞
] ⎠ −
L1(l−1) , L1(l−1)
] ⎠
− T+ 1(l−1) , T1(l−1) ,
⎛ [
. . .
⎝ [
⎝ [
.
⎞
] ⎠ −
+
⎞
⎛ [
..
] −
⎛ [
Lk2 , Lk2 +
]
] ⎠ −
+
.
⎞
] ⎠ −
T2j , T2j , −
. . .
Li2 , Li2 +
···
⎞
Al
]
⎛ [
L2j , L2j
⎛ [
] ⎠ −
⎞
] ⎠ −
+
.
⎞
. . .
⎝ [
⎝ [
T+ 1j , T1j ,
+
Al −1
···
] −
L1j , L1j
⎛ [
L22 , L22
⎛ [
⎛ [
⎝ [
L12 , L12
⎛ [ ⎝ [
Aj
···
] −
99
] ⎠ −
(25)
Box I.
IVIFS-SE can be expressed as in Eq. (27).
(
Ej =
−
−
m ˜ ˜ ˜ 1 ∑ Uij − Nij − Hij
m
−
)
+ ˜ij + − H ˜ij + + U˜ij − N
2
i=1
WjO = ∑n
(
1 − Ej
j=1
(
1 − Ej
);
n ∑
Wj = 1
) (27)
(28)
j=1
Where, Ej and Wj is the entropy value and weight of the attribute respectively. A smaller entropy value represents a high
entropy weight, and a greater entropy value represents a low entropy weight. Further, the ranking of the objective weights was taken as an input to determine the subjective weights of the QoS attributes. For the same, rank-order centroid, a subjective weight method was used since it reduces the maximum error of each QoS attribute weight via. ascertaining the centroid of all possible QoS attributes weights and maintains the rank order of objective weight method. Suppose there are n attributes, then the attribute ranked at jth position has the weight value mentioned in Eq. (29).
100
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
WjS =
Table 3 Crisp performance matrix CSP15×4 .
n 1∑ 1
n
(29)
rk
k=j
The integrated weights of the QoS attributes were computed using Eq. (30). It reflects the subjective considerations of the Decision Maker (DM) and the objective information. Wj = m ∗ WjO + n ∗ WjS
(30)
where, Wj indicates the integrated weight of the attribute; m and n represents the objective and subjective weights of the attributes and m, n ∈ [0, 1] respectively. In general, the attribute weight reflects the degree of importance of each attribute in evaluating the performance of each CSP in the cloud service selection problem. Higher weight of the attribute indicates high probability i.e., most important attribute. 4.2.3. Phase 3-ranking CSPs The ranking phase of IIVIFS-WASPAS uses WASPAS method to rank the CSPs due to its ability to provide accurate CSP ranking in various selection problems like supplier selection, logistic selection, hotel selection, etc. The WASPAS approach is a generalized approach of WSM and WPM methods. The steps involved in the WASPAS for service ranking are detailed below: Step-1: Compute the Relative Importance of ith CSP based on the WSM and WPM: The total relative importance of the ith CSP based on WSM and WPM is calculated using Eqs. (31) and (32) respectively. n ∑
WSMi = Pi =
˜ ij .Wj = Ƞ
n ∑ ([
j=1
´+ ´− ´+ ´− ´+ ´− U ij , Uij , Nij , Nij , Hij , Hij
] [
] [
])
j=1
(31)
´+ where, U = 1− ij
(
˜− Wj 1 − T ij
(
) + δ
(
˜ ij Wj 1 − T
))1/δ
)δ
))1/δ
´− , U = 1− − Wj − 1 ij ( ( ) ( ))1/δ δ = Wj L˜ + − Wj − 1 , ij
(
( ´+ − Wj − 1 , N ij ( ( ) ) 1 / δ ( ) δ − − ´ ij = Wj L˜ ij − Wj − 1 ´− ´ ij+ = 1 − U´ − ´+ N ,H ij − Nij and Hij = ´+ ´+ 1−U ij − Nij (
n ( )Wj ∏ ˜ ij Ƞ
WPMi = Ji =
j=1
=
n ([ ∏
] [ ] [ ]) + − + − Uij , Uij , Nij , Nij , Hij , Hij +
−
(32)
CSPs
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
QoS attributes/Attributes/Criteria AV
RT
P
S
SS
F
Eu
TS
CS
5 5 3 5 5 5 4 5 3 5 2 5 3 5 5
5 5 3 4 5 5 4 5 4 4 3 4 3 5 5
5 5 3 4 5 5 4 5 4 4 2 4 3 4 4
3 4 4 4 5 5 4 5 3 1 3 5 3 5 5
5 4 5 3 4 5 4 5 4 4 3 5 2 5 4
5 5 2 4 5 5 5 5 3 4 3 5 3 5 4
5 5 2 5 5 5 5 5 5 1 3 5 3 5 5
5 5 2 5 5 5 4 4 4 1 2 4 4 5 5
5 5 2 5 5 5 4 4 4 1 3 4 3 5 5
Table 4 Normalized crisp performance matrix. CSPs
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
QoS attributes/ Attributes/Criteria AV
RT
P
S
SS
F
EU
TS
CS
1 1 0.6 1 1 1 0.8 1 0.6 1 0.4 1 0.6 1 1
1 1 0.6 0.8 1 1 0.8 1 0.8 0.8 0.6 0.8 0.6 1 1
1 1 0.6 0.8 1 1 0.8 1 0.8 0.8 0.4 0.8 0.6 0.8 0.8
0.6 0.8 0.8 0.8 1 1 0.8 1 0.6 0.2 0.6 1 0.6 1 1
1 0.8 1 0.6 0.8 1 0.8 1 0.8 0.8 0.6 1 0.4 1 0.8
1 1 0.4 0.8 1 1 1 1 0.6 0.8 0.6 1 0.6 1 0.8
1 1 0.4 1 1 1 1 1 1 0.2 0.6 1 0.6 1 1
1 1 0.4 1 1 1 0.8 0.8 0.8 0.2 0.4 0.8 0.8 1 1
1 1 0.4 1 1 1 0.8 0.8 0.8 0.2 0.6 0.8 0.6 1 1
transformed into WSM and WPM respectively
⏐ ⏐ ⏐∑ ⏐ ⏐ ⏐ ⏐ Ji ⏐ ⏐ ⏐ ⏐⏐ ƥ = ⏐0.5 − ⏐∑ ∑ ⏐ .Pi + Ji ⏐ ⏐ ⏐
(34)
Step-3: Rank the CSPs. The preference attitude of the decision experts reflected by the preference attitudinal score and accuracy degree is computed (Eqs. (24) and (20)) and the CSPs are ranked in decreasing order, i.e., rank 1 represents the trustworthy CSP.
j=1
( ( )δ ( ))1/δ − ˜− − Wj − 1 , Uij = Wj T − ij ( ) 1 /δ ( ) ( ) ( ))1/δ + δ ˜+ Wj − 1 , Nij = 1 − Wj 1 − L − Wj − 1 , N− ij ij = ( ( ) 1 / δ )δ ( ) − + − − ˜ ij − Wj − 1 1 − Wj 1 − L , Hij = 1 − Uij − Nij and where, U+ = ij
−
+
(
˜+ Wj T ij
(
)δ
+
Hij = 1 − Uij − Nij . The summation and product of all the attributes are computed using Schweizer-Sklar operations (Eqs. (5)–(7)). Step-2: Calculate the total relative importance for each CSP (alternative). A generalized criterion of WASPAS is calculated based on the additive method of WSM and the multiplicative method of WPM for each CSP using Eq. (33).
WASPASi = Yi
= ƥ. Pi + (1 − ƥ) Ji =
([
− − U+ , N+ , Hi+ , Hi− i , Ui i , Ni
] [
] [
])
(33)
Where, ƥ is the parameter of the WASPAS method (Eq. (34)) and ƥ ∈ [0, 1]. If ƥ = 1 and ƥ = 0, the WASPAS method is
5. Case study The performance of IIVIFS-WASPAS, the proposed cloud service selection methodology has been evaluated using a sample dataset extracted from the Cloud Armor project, University of Adelaide [61], a real-world trust feedback dataset which focus on the development of a robust trust management framework for the cloud environment. It contains 10,080 user feedbacks for nine QoS attributes (Benefit attribute: Availability (AV), Response Time (RT), Security (Sec), Speed (S), Storage Space (SS), Features (F), Ease-of-use (Eu), Technical Support (TS), Customer Service (CS) and Level of Expertise (LoE); Cost attribute: Price (P)) provided by nearly 7000 consumers for 114 real-world cloud services. The user feedbacks were obtained from the major review websites like Cloud Hosting Reviews, Cloud Service Providers, Cloud Storage Reviews, and Ratings during the period July 2003 to June 2012 at different timestamps. The sample trust feedback dataset considered for the case study comprises users’ feedbacks for fifteen CSPs namely,
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
101
Table 5 IVIFS performance matrix (IVIFS 15×9 ). CSPs
QoS attributes AV
RT
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.515, 0.615] , [0.365, 0.385]
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{ CSP1
{ CSP2 CSP3 CSP4 CSP5
{ CSP6
{ CSP7
{ CSP8
{ CSP9
{ CSP10 CSP11 CSP12
{ CSP13
{ CSP14
{ CSP15 CSPs/Alternatives
}
}
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.515, 0.615] , [0.365, 0.385]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.875, 0.975] , [0.005, 0.025]
}
}
}
}
TS
CS
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.335, 0.435] , [0.545, 0.565]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
[0.515, 0.615] , [0.365, 0.385]
{
[0.875, 0.975] , [0.005, 0.025]
{
[0.695, 0.795] , [0.185, 0.205]
{
[0.695, 0.795] , [0.185, 0.205]
[0.695, 0.795] , [0.185, 0.205]
{
[0.155, 0.255] , [0.725, 0.745]
{
[0.155, 0.255] , [0.725, 0.745]
{
[0.155, 0.255] , [0.725, 0.745]
[0.515, 0.615] , [0.365, 0.385]
{
[0.515, 0.615] , [0.365, 0.385]
{
[0.335, 0.435] , [0.545, 0.565]
{
[0.515, 0.615] , [0.365, 0.385]
CSP4
{ { { { { { { CSP11
{
[0.875, 0.975] , [0.005, 0.025]
CSP3
CSP10
}
EU
{
CSP9
[0.875, 0.975] , [0.005, 0.025]
{
CSP2
CSP8
{
}
CSP1
CSP7
SS
) [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.155, 0.255] , [0.725, 0.745] { } [0.515, 0.615] , [0.365, 0.385] { } [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] (
[0.875, 0.975] , [0.005, 0.025]
{
CSP6
S
} [0.875, 0.975] , [0.005, 0.025] ( ) [0.875, 0.975] , [0.005, 0.025] { } [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.875, 0.975] , [0.005, 0.025] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205] { } [0.335, 0.435] , [0.545, 0.565] { } [0.695, 0.795] , [0.185, 0.205] { } [0.515, 0.615] , [0.365, 0.385] { } [0.695, 0.795] , [0.185, 0.205] { } [0.695, 0.795] , [0.185, 0.205]
Criteria/Attributes F
CSP5
P
{
}
}
}
}
}
}
}
}
}
}
}
}
(continued on next page)
102
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Table 5 (continued). CSPs/Alternatives
Criteria/Attributes F
EU
[0.875, 0.975] , {[0.005, 0.025] } [0.515, 0.615] , [0.365, 0.385]
{
CSP12 CSP13
TS
}
[0.875, 0.975] , {[0.005, 0.025] } [0.515, 0.615] , [0.365, 0.385]
{
CS
}
[0.695, 0.795] , {[0.185, 0.205] } [0.695, 0.795] , [0.185, 0.205]
{
}
[0.695, 0.795] , {[0.185, 0.205] } [0.515, 0.615] , [0.365, 0.385]
{
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.695, 0.795] , [0.185, 0.205]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
{
[0.875, 0.975] , [0.005, 0.025]
}
CSP14 CSP15
Table 6 Normalized IVIFS performance matrix (IVIFS 15×9 ). CSPs
CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
QoS attributes AV
RT
P
SP
SS
⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1535, 0.1755] ,⎬ [0.1489, 0.1650] , ⎩[0.6594, 0.6976] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎫ ⎧ ⎨[0.0740, 0.0961] ,⎬ [0.4387, 0.4548] , ⎩[0.4492, 0.4873] ⎭ ⎫ ⎧ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭ ⎧ ⎫ ⎨[0.1137, 0.1358] ,⎬ [0.2938, 0.3099] , ⎩[0.5543, 0.5925] ⎭ ⎫ ⎧ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭
⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎫ ⎧ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1573, 0.1799] ,⎬ [0.1668, 0.1848] , ⎩[0.6352, 0.6759] ⎭ ⎧ ⎫ ⎨[0.1166, 0.1392] ,⎬ [0.3291, 0.3471] , ⎩[0.5137, 0.5543] ⎭ ⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭
⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1215, 0.1451] ,⎬ [0.2786, 0.2939] , ⎩[0.5611, 0.5999] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.2064, 0.2300] ,⎬ [0.00380.0191] , ⎩[0.7509, 0.7898] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎧ ⎫ ⎨[0.0790, 0.1026] ,⎬ [0.4160, 0.4313] , ⎩[0.4661, 0.5050] ⎭ ⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭ ⎫ ⎧ ⎨[0.1215, 0.1451] ,⎬ [0.2786, 0.2939] , ⎩[0.5611, 0.5999] ⎭ ⎫ ⎧ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭
⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.1665, 0.1905] ,⎬ [0.1166, 0.1293] , ⎩[0.6803, 0.7168] ⎭ ⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭ ⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.0371, 0.0611] ,⎬ [0.4571, 0.4697] , ⎩[0.4692, 0.5057] ⎭ ⎧ ⎫ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎫ ⎧ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭ ⎫ ⎧ ⎨[0.1234, 0.1473] ,⎬ [0.2301, 0.2428] , ⎩[0.6099, 0.6465] ⎭ ⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭
⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1195, 0.1427] ,⎬ [0.2850, 0.3006] , ⎩[0.5567, 0.5955] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭ ⎫ ⎧ ⎨[0.1195, 0.1427] ,⎬ [0.2850, 0.3006] , ⎩[0.5567, 0.5955] ⎭ ⎫ ⎧ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ ⎧ ⎫ ⎨[0.0777, 0.1009] ,⎬ [0.4255, 0.4411] , ⎩[0.4580, 0.4968] ⎭ ⎫ ⎧ ⎨[0.2030, 0.2262] ,⎬ [0.0039, 0.0195] , ⎩[0.7543, 0.7931] ⎭ (continued on next page)
Backupgenie (CSP1 ), Bluehost (CSP2 ), Carbonite (CSP3 ), Elephantdriv e (CSP4 ), GoDaddy (CSP5 ), ibackup (CSP6 ), idriv e (CSP7 ), justcloud (CSP8 ), keepit (CSP9 ), liv edriv e (CSP10 ), Mozy (CSP11 ), MyPCBackup (CSP12 ), sos − online − backup (CSP13 ), SugarSync (CSP14 ), and
yousendit − online − backup (CSP15 ) provided for nine QoS attributes namely, AV , RT , P , S , SS , F , Eu, TS and CS. The user feedback ranges from 1 to 5, where 1 represents the most insignificant feedback and 5 represents the most significant feedback. For the construction of a complete user-service trust feedback
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
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Table 6 (continued). CSPs
QoS attributes AV
RT
P
SP
SS
CSP15
⎧ ⎫ ⎨[0.1932, 0.2153] ,⎬ [0.0040, 0.0201] , ⎩[0.7646, 0.8028] ⎭
⎧ ⎫ ⎨[0.1981, 0.2207] ,⎬ [0.0045, 0.0225] , ⎩[0.7568, 0.7974] ⎭
⎧ ⎫ ⎨[0.1639, 0.1875] ,⎬ [0.1412, 0.1565] , ⎩[0.6560, 0.6949] ⎭
⎧ ⎫ ⎨[0.2096, 0.2336] ,⎬ [0.0032, 0.0158] , ⎩[0.7506, 0.7872] ⎭
⎧ ⎫ ⎨[0.1613, 0.1845] ,⎬ [0.1444, 0.1601] , ⎩[0.6555, 0.6943] ⎭
CSPs
CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
CSP15
QoS attributes F
Eu
TS
CS
⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.0762, 0.0990] ,⎬ [0.4187, 0.4340] , ⎩[0.4670, 0.5051] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1421, 0.1575] , ⎩ ⎭ ⎧[0.6616, 0.6997] ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1575, 0.1421] , ⎩[0.6770, 0.6843] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎧ ⎫ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1172, 0.1400] ,⎬ [0.2804, 0.2958] , ⎩[0.5643, 0.6024] ⎭ ⎫ ⎧ ⎨[0.1991, 0.2219] ,⎬ [0.0038, 0.0192] , ⎩[0.7589, 0.7970] ⎭ ⎧ ⎫ ⎨[0.1582, 0.1809] ,⎬ [0.1575, 0.1421] , ⎩[0.6770, 0.6843] ⎭
⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.0739, 0.0959] ,⎬ [0.3620, 0.3753] , ⎩[0.5288, 0.5641] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩ ⎭ ⎧[0.7683, 0.8037] ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.0342, 0.0562] ,⎬ [0.4815, 0.4948] , ⎩[0.4490, 0.4843] ⎭ ⎧ ⎫ ⎨[0.1136, 0.1356] ,⎬ [0.2424, 0.2557] , ⎩[0.6086, 0.6440] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎧ ⎫ ⎨[0.1136, 0.1356] ,⎬ [0.2424, 0.2557] , ⎩[0.6086, 0.6440] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭ ⎫ ⎧ ⎨[0.1930, 0.2150] ,⎬ [0.0033, 0.0166] , ⎩[0.7683, 0.8037] ⎭
⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.0784, 0.1017] ,⎬ [0.3317, 0.3439] , ⎩[0.5543, 0.5899] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎭ ⎩ ⎧[0.7567, 0.7923] ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.0363, 0.0596] ,⎬ [0.4413, 0.4535] , ⎩[0.4869, 0.5224] ⎭ ⎧ ⎫ ⎨[0.0784, 0.1017] ,⎬ [0.3317, 0.3439] , ⎩[0.5543, 0.5899] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎧ ⎫ ⎨[0.1625, 0.1859] ,⎬ [0.1126, 0.1248] , ⎩[0.6893, 0.7248] ⎭ ⎫ ⎧ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭ ⎧ ⎫ ⎨[0.2046, 0.2280] ,⎬ [0.0030, 0.0152] , ⎩[0.7567, 0.7923] ⎭
⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.0786, 0.1021] ,⎬ [0.3400, 0.3525] , ⎩[0.5454, 0.5814] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩ ⎭ ⎧[0.7556, 0.7915] ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.0364, 0.0599] ,⎬ [0.4523, 0.4648] . ⎩[0.4754, 0.5113] ⎭ ⎧ ⎫ ⎨[0.1209, 0.1444] ,⎬ [0.2277, 0.2402] , ⎩[0.6155, 0.6514] ⎭ ⎧ ⎫ ⎨[0.1631, 0.1866] ,⎬ [0.1154, 0.1279] , ⎩[0.6855, 0.7215] ⎭ ⎧ ⎫ ⎨[0.1209, 0.1444] ,⎬ [0.2277, 0.2402] , ⎩[0.6155, 0.6514] ⎭ ⎫ ⎧ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭ ⎧ ⎫ ⎨[0.2054, 0.2288] ,⎬ [0.0031, 0.0156] , ⎩[0.7556, 0.7915] ⎭
Table 7 Entropy values and weights for each attribute. Ej Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.6445 0.1117 4
0.6410 0.1128 1
0.6429 0.1122 2
0.6488 0.1103 6
0.6432 0.1121 3
0.6445 0.1117 5
0.6502 0.1099 7
0.6515 0.1095 9
0.6503 0.1099 8
dataset, the feedback entries with missing values and redundant CSPs feedback entries were removed. The degree of dependency among the QoS attributes was checked using the chi-square test with (r − 1, c − 1) degrees of freedom where, r represents the
number of cloud service providers and c represents the number of QoS attributes.
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 8 Subjective weights for each attribute. Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.1342 4
0.2002 1
0.1783 2
0.0900 6
0.1563 3
0.1121 4
0.0676 7
0.0226 9
0.0451 8
Table 9 The integrated weights for each attribute and their ranking. Wj Rank
AV
RT
P
S
SS
F
EU
TS
CS
0.1229 4
0.1565 1
0.1452 2
0.1002 6
0.1342 3
0.1119 5
0.0887 7
0.0660 9
0.0775 8
Table 10 IVIFS-WSM and IVIFS-WPM for cloud service providers. CSPs CSP1
CSP2
CSP3
CSP4
CSP5
CSP6
CSP7
CSP8
CSP9
CSP10
CSP11
CSP12
CSP13
CSP14
CSP15
IVIFS-WSM (Pi )
IVIFS-WPM (Ji )
IVIFS-WASPAS
⎧ ⎫ ⎨[0.1939, 0.2169] ,⎬ [0.0039, 0.0196] , ⎩[0.7634, 0.8022] ⎭ ⎧ ⎫ ⎨[0.1922, 0.2152] ,⎬ [0.0042, 0.0211] , ⎩[0.7637, 0.8036] ⎭ ⎧ ⎫ ⎨[0.1233, 0.1465] ,⎬ [0.0106, 0.0523] , ⎩[0.8012, 0.8661] ⎭ ⎧ ⎫ ⎨[0.1702, 0.1933] ,⎬ [0.0057, 0.0283] , ⎩[0.7700, 0.8241] ⎭ ⎧ ⎫ ⎨[0.1964, 0.2194] ,⎬ [0.0039, 0.0194] , ⎩[0.7611, 0.7997] ⎭ ⎧ ⎫ ⎨[0.2017, 0.2247] ,⎬ [0.0037, 0.0183] , ⎩[0.7570, 0.7947] ⎭ ⎧ ⎫ ⎨[0.1687, 0.1197] ,⎬ [0.0080, 0.0389] , ⎩[0.7694, 0.8233] ⎭ ⎧ ⎫ ⎨[0.1959, 0.2190] ,⎬ [0.0041, 0.0204] , ⎩[0.7606, 0.8000] ⎭ ⎧ ⎫ ⎨[0.1509, 0.1740] ,⎬ [0.0111, 0.534] , ⎩[0.7726, 0.8379] ⎭ ⎧ ⎫ ⎨[0.1297, 0.1528] ,⎬ [0.0115, 0.0554] , ⎩[0.7917, 0.8589] ⎭ ⎧ ⎫ ⎨[0.1055, 0.1286] ,⎬ [0.2950, 0.3102] , ⎩[0.5612, 0.5995] ⎭ ⎫ ⎧ ⎨[0.1838, 0.2068] ,⎬ [0.0049, 0.0242] , ⎩[0.7690, 0.8114] ⎭ ⎧ ⎫ ⎨[0.1165, 0.1395] ,⎬ [0.2425, 0.2594] , ⎩[0.6011, 0.6410] ⎭ ⎧ ⎫ ⎨[0.1958, 0.2188] ,⎬ [0.0039, 0.0196] , ⎩[0.7616, 0.8003] ⎭ ⎧ ⎫ ⎨[0.1860, 0.2090] ,⎬ [0.0045, 0.0226] , ⎩[0.7684, 0.8095] ⎭
⎧ ⎫ ⎨[0.1852, 0.2095] ,⎬ [0.0359, 0.0508] , ⎩[0.7397, 0.7789] ⎭ ⎧ ⎫ ⎨[0.1887, 0.2120] ,⎬ [0.0392, 0.0543] , ⎩[0.7337, 0.7721] ⎭ ⎧ ⎫ ⎨[0.1018, 0.1271] ,⎬ [0.2944, 0.3099] , ⎩[0.5630, 0.6038] ⎭ ⎧ ⎫ ⎨[0.1616, 0.1855] ,⎬ [0.1295, 0.1451] , ⎩[0.6693, 0.7089] ⎭ ⎧ ⎫ ⎨[0.1934, 0.2165] ,⎬ [0.0267, 0.0419] , ⎩[0.7416, 0.7799] ⎭ ⎧ ⎫ ⎨[0.2006, 0.2236] ,⎬ [0.0038, 0.0188] , ⎩[0.7576, 0.7956] ⎭ ⎧ ⎫ ⎨[0.1659, 0.1891] ,⎬ [0.1180, 0.1333] , ⎩[0.6777, 0.7161] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2162] ,⎬ [0.0223, 0.0372] , ⎩[0.7466, 0.7847] ⎭ ⎧ ⎫ ⎨[0.1430, 0.1668] ,⎬ [0.1852, 0.2006] , ⎩[0.6326, 0.6718] ⎭ ⎧ ⎫ ⎨[0.0596, 0.0936] ,⎬ [0.2961, 0.3112] , ⎩[0.5952, 0.6444] ⎭ ⎧ ⎫ ⎨[0.0979, 0.1221] ,⎬ [0.3319, 0.3475] , ⎩[0.5303, 0.5702] ⎭ ⎫ ⎧ ⎨[0.1791, 0.2025] ,⎬ [0.0732, 0.0885] , ⎩[0.7090, 0.7477] ⎭ ⎫ ⎧ ⎨[0.1101, 0.1341] ,⎬ [0.2982, 0.3138] , ⎩[0.5521, 0.5917] ⎭ ⎧ ⎫ ⎨[0.1930, 0.2162] ,⎬ [0.0279, 0.0430] , ⎩[0.7408, 0.7791] ⎭ ⎫ ⎧ ⎨[0.1814, 0.2047] ,⎬ [0.0657, 0.0809] , ⎩[0.7144, 0.7529] ⎭
⎧ ⎫ ⎨[0.1882, 0.2120] ,⎬ [0.0067, 0.0298] , ⎩[0.7582, 0.8051] ⎭ ⎧ ⎫ ⎨[0.1899, 0.2131] ,⎬ [0.0072, 0.0319] , ⎩[0.7550, 0.8029] ⎭ ⎧ ⎫ ⎨[0.1092, 0.1338] ,⎬ [0.0184, 0.0879] , ⎩[0.7783, 0.8725] ⎭ ⎧ ⎫ ⎨[0.1645, 0.1882] ,⎬ [0.0098, 0.0471] , ⎩[0.7648, 0.8257] ⎭ ⎧ ⎫ ⎨[0.1944, 0.2175] ,⎬ [0.0066, 0.0281] , ⎩[0.7544, 0.7990] ⎭ ⎧ ⎫ ⎨[0.2010, 0.2240] ,⎬ [0.0037, 0.0186] , ⎩[0.7574, 0.7953] ⎭ ⎧ ⎫ ⎨[0.1668, 0.1899] ,⎬ [0.0137, 0.0621] , ⎩[0.7479, 0.8194] ⎭ ⎧ ⎫ ⎨[0.1940, 0.2171] ,⎬ [0.0068, 0.0279] , ⎩[0.7550, 0.7992] ⎭ ⎧ ⎫ ⎨[0.1457, 0.1692] ,⎬ [0.0191, 0.0863] , ⎩[0.7444, 0.8352] ⎭ ⎧ ⎫ ⎨[0.0849, 0.1148] ,⎬ [0.0198, 0.0929] , ⎩[0.7923, 0.8953] ⎭ ⎧ ⎫ ⎨[0.1005, 0.1243] ,⎬ [0.3180, 0.3335] , ⎩[0.5421, 0.5815] ⎭ ⎧ ⎫ ⎨[0.1807, 0.2039] ,⎬ [0.0084, 0.0390] , ⎩[0.7570, 0.8109] ⎭ ⎫ ⎧ ⎨[0.1123, 0.1360] ,⎬ [0.2755, 0.2919] , ⎩[0.5721, 0.6123] ⎭ ⎫ ⎧ ⎨[0.1940, 0.2171] ,⎬ [0.0066, 0.0285] , ⎩[0.7544, 0.7994] ⎭ ⎧ ⎫ ⎨[0.1829, 0.2062] ,⎬ [0.0078, 0.0363] , ⎩[0.7575, 0.8093] ⎭
(i) Construction of IVIFS Performance Matrix Initially, the performance matrix (CSP15×9 ) was generated for fifteen cloud service providers (Alternatives) and nine QoS attributes (Criteria) using the crisp numbers (Table 3). The crisp
performance matrix (CSP15×9 ) in Table 3 was converted into normalized crisp values (Table 4).
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 11 Cloud service providers ranking. CSPs
degree (Score ) Siρ (δ)
Accuracy ( ) degree Aiρ (δ)
Uncertainty ( ) degree Ui
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
0.3006 0.3005 0.1900 0.2676 0.3071 0.3197 0.2594 0.3067 0.2240 0.1665 −0.1092 0.2875 −0.0534 0.3064 0.2914
0.5939 0.5930 0.6085 0.5984 0.5922 0.5921 0.5946 0.5924 0.5966 0.6146 0.5206 0.5947 0.5307 0.5923 0.5945
0.4061 0.4070 0.3915 0.4016 0.4078 0.4079 0.4054 0.4076 0.4034 0.3854 0.4794 0.4053 0.4693 0.4077 0.4055
105
Among the nine QoS attributes, the most important QoS attributes are Response Time (RT) and Price (P), whereas the least important QoS attribute is Technical Support (TS). (iii) Compute the Relative Importance of CSPs The relative importance of the considered CSPs based on WSM (Eq. (31)), WPM (Eq. (32)) and the total relative importance of each CSP was determined using generalized WASPAS measure (Eq. (33)) (Table 10). The parameter (ƥ) value was derived using Eq. (34).
⏐ ⏐ ƥ = ⏐⏐0.5 −
1.7952
⏐ ⏐ ⏐ = |0.5 − 0.2| = 0.3 9.1139 + 1.7952 ⏐
Table 11 presents the score, accuracy and uncertainty degree (Ui =1-Aiρ (δ)) of CSPs in the range of [0, 1]. ( i The) service ranking with respect to the (i) Score degree Sρ (δ) : CSP 6 > CSP5 > CSP8 > CSP14 > CSP1 > CSP2 > CSP15 > CSP13 > CSP4 > CSP7 (> CSP9) > CSP3 > CSP10 > CSP13 > CSP11 , (ii) Accuracy degree Aiρ (δ) : CSP 10 > CSP3 > CSP4 > CSP9 > CSP12 > CSP7 > CSP15 > CSP1 > CSP2 > CSP8 > CSP ( 14 ) > CS5 > CSP6 > CSP13 > CSP11 and (iii) Uncertainty degree Ui : : CSP 10 > CSP3 > CSP4 > CSP9 > CSP12 > CSP7 > CSP15 > CSP1 > CSP2 > CSP8 > CSP14 > CS5 > CSP6 > CSP13 > CSP11 . 5.1. Performance validation The effectiveness of IIVIFS-WASPAS, the proposed cloud service selection approach over the state-of-the-art IVIFS based cloud service selection approaches was validated using a three stage empirical model in terms of cardinal ranking, sensitivity analysis, and rank reversal phenomenon.
Fig. 3. CSPs ranking acceptability indices with respect to decision mechanism coefficient.
Further, the normalized crisp performance matrix (Table 4) was converted into their corresponding IVIFN using the conversion rule given in Table 2. Table 5 presents the IVIFS performance matrix (IVIFS )15×9 for fifteen cloud service providers and nine QoS attributes. The hesitancy degree for a given MDF ( corresponding ) and NDF for IVIFSij 15×9 is [0.000, 0.120] which is obtained using Eq. (3). The IVIFS performance matrix was normalized using Eq. (26) to construct the normalized IVIFS performance matrix (IVIFS )15×9 (Table 6). (ii) Determine Weights of the QoS Attributes ( ) The objective and subjective weights of each attribute Wj was determined using modified IVIFS-SE (Eqs. (27)–(28)) and rank-centroid approach (Eq. (29)). A hybrid weight assessment model (Eq. (30)) was used to determine the weights of the QoS attributes which are then used to evaluate the CSPs for the identification of TCSPs and derive accurate service ranking. Table 7 presents the entropy values and their corresponding QoS attributes weights and rank in an increasing order. The subjective weights of the QoS attributes using the subjective weight assessment method, i.e., rank-centroid method is given in Table 8. Further, the integrated weights of the QoS attributes are given in Table 9.
5.1.1. Cardinal rankings of the state-of-the-art IVIFS based cloud service provider selection approach for the selection of TCSPs IIVIFS-WASPAS, the proposed cloud service provider selection approach which integrates a hybrid weight model and IVIFSWASPAS for the identification of TCSPs with accurate service ranking was compared with the state-of-the-art IVIFS service selection approaches like IVIFS-Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) plus full MULTIplicative form (MULTI) (IVIFS-MULTIMOORA) [36], IVIFS-TOPSIS [62], IVIFSVlsekriterijumska Optimizacija I KOmpromisno Resenje (IVIFSVIKOR) [36], and IVIFS-Complex Proportional Assessment of alternativeS (IVIFS-COPRAS) [36] based on the Spearman’s rank correlation analysis (ρr ). From Table 12, it was evident that ibackup (CSP 6 ) is the optimal trustworthy cloud service provider based on the service ranking provided by the IIVIFS and the stateof-the-art IVIFS based service selection approach. Even though, the other MCDM approaches listed in Table 12 were used to solve the cloud service selection problem they are inefficient in providing accurate service ranking on the addition or removal of the best service provider (ibackup) or the worst service provider (Mozy) respectively. Spearman’s rank correlation analysis (ρr ), a non-parametric test was employed to validate the correctness of the ranking provided by the IIVIFS and the state-of-the-art IVIFS based cloud service selection approaches (Eq. (35)).
ρr = 1 −
6
∑
d2i
m (m − 1)
(35)
Where, m is the number of alternatives, di is the difference between the ranks of any two MCDM approaches. Table 13 presents the interpretation of different values of ρr [63]. From the Table 13, it was evident that if the Spearman rank correlation (ρr ) is higher than 0.6, then there is a high statistical dependency among the considered IVIFS approaches.
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O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 12 Comparison of trustworthy CSPs ranking. CSPs
IIVIFSWASPAS
IVIFSMULTIMOORA [36]
IVIFSTOPSIS [62]
IVIFSVIKOR [36]
IVIFSCOPRAS [36]
CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 CSP9 CSP10 CSP11 CSP12 CSP13 CSP14 CSP15
5 6 12 9 2 1 10 3 11 13 15 8 14 4 7
5 6 13 9 2 1 10 4 11 12 15 8 14 3 7
5 6 13 9 3 1 10 2 11 12 15 8 14 4 7
6 5 13 10 3 1 9 2 11 12 15 8 14 4 7
5 6 13 9 2 1 10 4 11 12 15 8 14 3 7
Table 13 Spearman’s rank correlation analysis range. Correlation analysis range
Interpretation
0.8 0.6 0.4 0.2
Very strong Strong Average Weak Very weak
< ρr < ρr < ρr < ρr ρr ≤ 0.2
≤ 1.0 ≤ 0.8 ≤ 0.6 ≤ 0.4
Table 14 presents the rank correlation analysis between IIVIFSWASPAS and the state-of-the-art IVIFS based service selection approaches. From Table 14, it was found that the rank correlation analysis for most of the IVIFS approaches was greater than 0.7. Therefore, we state that the service ranking provided by the IIVIFS-WASPAS is consistent with the considered IVIFS-MCDM based service selection approaches. 5.1.2. Sensitivity analysis In order to increase accuracy and efficiency of the IIVIFSWASPAS, the impact of the change in coefficient (ƥ) value is examined. The coefficient (ƥ) value was computed using Eq. (34) which lies in the range of [0, 1] with the step size of 0.1. Fig. 3 represents the relative values of the CSPs by varying the coefficient value (from ƥ = 0.1 to ƥ = 1) while retaining the same QoS attributes weights in order to obtain stability of CSP ranking. The service ranking obtained by varying the coefficient (ƥ) value (from 0 to 1) was ordered as ibackup > justcloud > GoDaddy > SugarSync > Backupgenie > Bluehost > MyPCBackup > Yousendit − online − backup > Elephantdriv e > idriv e > Keepit > Carbonite > Liv edriv e > Sos − online − backup > Mozy. The relative values of the fifteen CSPs increase by 0.0821, 0.0829, 0.09, 0.0832, 0.0825, 0.0824, 0.0846, 0.0827, 0.0871, 0.0894, 0.0929, 0.0825, 0.0914, 0.0816, and 0.0822 with the increase in the ƥ value. From the above series of improvement in the relative values of CSPs, we conclude that ibackup(CSP 6 ) is the trustworthy cloud service provider since it has the minimal fluctuations in the relative value. Subsequently, the sensitivity analysis has been carried by varying the different criterion weights in order to maintain the robustness of the proposed methodology (IIVIFS-WASPAS). For instance, the CSP ranking does not vary on interchanging the weights C1 with C2 while keeping the weights of the remaining criteria (C3 to C9 ) as constant. Similarly, the weights of the other criteria can be interchanged and their respective impact on the service ranking can be analysed. Fig. 4 demonstrates the sensitivity of the CSP ranking to the changes in the weights of the QoS attributes for 4 cases (C 1 − C 2, C 2 − C 8, C 3 − C 7 and C 3 − C 4).
5.1.3. Rank Reversal Phenomenon (RRP) In the literature, several MCDM approaches have been used for effective decision making for the identification of TCSPs. Despite the advantages of these approaches, they are inefficient in preventing the Rank Reversal Phenomenon (RRP) due to mutual correlation(s) among the relevant and irrelevant CSPs, i.e., change in the set of candidate CSPs. This is due to the use of improper normalization technique [64] in several MCDM methods like AHP (Min–max normalization), PROMETHEE (Preference Ranking Organization Method of Enrichment Evaluations-linear normalization), TOPSIS (vector normalization), ELECTRE (Elimination and Choice Expressing REality-linear normalization), MULTIMOORA (target-based normalization), DEA (Data Envelopment Analysislinear normalization), etc. IIVIFS-WASPAS, the proposed service selection approach addresses the RRP problem through proximity index and thereby obtains consistent ranking by minimizing the RRP. For instance, the preference/ranking order of cloud service providers remains same after the addition of best service provider (ibackup) and/or the deletion of an existing service provider (Liv edriv e). Fig. 5 presents the ranking of fourteen CSPs after the removal of worst CSP (Mozy). 6. Conclusions ‘Service Selection Problem’ remains a challenging research area in the field of cloud computing due to the emerging new cloud service providers with different functionalities and dynamic user requirements. Further, the uncertainty in the objective and subjective assessment data, a primary source for cloud service evaluation complicates the service selection problem. To address the same, this work presents Improved Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregated Sum and Product Assessment (IIVIFS-WASPAS) based cloud service selection approach for the identification of the trustworthy CSPs. IIVIFSWASPAS employs an integrated objective & subjective weight assessment approach and preference attitudinal score and accuracy function based IVIFS-WASPAS for weight assessment of the QoS attributes and service ranking respectively. Further, the uncertainty in the user preferences is captured by the IVIFS. The effectiveness of the IIVIFS-WASPAS cloud service provider selection approach was validated using a sample trust feedback dataset with fifteen CSPs and nine QoS attributes derived from the Cloud Armor trust feedback dataset in terms of sensitivity analysis and rank reversal phenomenon. The application of trust prediction and user-service based QoS value prediction, an integral part of any cloud service selection framework proves to be a challenging future research direction of this work.
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110 Table 14 Spearman’s rank correlation analysis. IIVIFS-WASPAS IVIFS-MULTIMOORA IVIFS-TOPSIS IVIFS-VIKOR IVIFS-COPRAS
IIVIFS-WASPAS
IVIFS-MULTIMOORA
IVIFS-TOPSIS
IVIFS-VIKOR
IVIFS-COPRA
– 0.89 0.89 0.77 0.89
0.89 – 0.83 0.71 1.00
0.89 0.83 – 0.89 0.83
0.77 0.71 0.89 – 0.71
0.89 1.00 0.83 0.71 –
Fig. 4. Robustness-Interchange of criterion weights.
Fig. 5. Ranking after the removal of worst CSP (Mozy).
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by The Council of Scientific & Industrial Research, India and The Department of Science & Technology, India (Grant No: CSIR - SRF Fellowship/143345/2K17/1 and SR/FST/ETI-349/2013). The authors gratefully acknowledge Tata Realty-IT City-SASTRA Srinivasa Ramanujan Research Cell of SASTRA Deemed University for the financial support extended to us in carrying out this research work.
Appendix
Abbreviations Abstract MCDM CSPs QoS IVIFS-WASPAS
TCSPs IIVIFS-WASPAS RRP
Explanation Multi-Criteria Decision Making Cloud Service Providers Quality of Service Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregate Sum and Product ASsessment Trustworthy CSPs Improved IVIFS-WASPAS Rank Reversal Phenomenon
107
108
1. Introduction ICT StaaS FMCDM IFS NFS HFS WSM WPM SE 2. Literature review FAHP-WASPAS NMCDA AHP 2sFL FAHP MATLAB FTOPSIS
GDM CCT PS IVIF AHP IVIF COPRAS IVIF MULTIMOORA
IVIF VIKOR FEA BSC FDM Cloud-FuSeR FLW MSER OMNeT++ CINS INS MAGDM TIFNs MCGDM FANP ELECTRE GRA ER CTE PI DI PD IVFS
O. Gireesha, N. Somu, K. Krithivasan et al. / Future Generation Computer Systems 103 (2020) 91–110
Information and Communication Technology Storage as a Service Fuzzy based MCDM Intuitionistic Fuzzy Set Neutrosophic Fuzzy Set Hesitant Fuzzy Set Weighted Sum Model Weighted Product Model Shannon Entropy Fuzzy Analytic Hierarchy Process-WASPAS Neutrosophic Multi-Criteria Decision Analysis Analytic Hierarchy Process two-stage Fuzzy Logic Fuzzy AHP MATrix LABoratory Fuzzy based Technique for Order of Preference by Similarity to Ideal Solution Group Decision Making Cloud Computing Technology Provider Selection Interval-Valued Intuitionistic Fuzzy AHP IVIF COmplex PRoportional ASsessment IVIF multi-objective optimization by ratio analysis plus the full multiplicative form IVIF VišekriterijumskoKompromisnoRangiranje Fuzzy Extent Analysis Balanced Score Card Fuzzy Delphi Method Fuzzy user-oriented cloud SeRvice selection Fuzzy LightWeight Mean Squared Error of Ranks Objective Modular Network testbed in C++ Cloud service Interval Neutrosophic Set Interval Neutrosophic Set Multi-Attribute Group Decision-Making Triangular Intuitionistic Fuzzy Numbers Multi-Criteria Group Decision Making Fuzzy Analytic Network Process Elimination and Choice Translating Reality Grey Relational Analysis Evidence Reasoning Cloud service Trustworthiness Evaluation Performance Importance Delivery Importance Performance Delivery Interval-Valued Fuzzy Set
3.1. Interval-Valued Intuitionistic Fuzzy Set (IVIFS) MDF Membership Degree Function NMDF Non-Membership Degree Function HDF Hesitant Degree Function IFN Intuitionistic Fuzzy Number HD Hesitancy Degree IVIFV Interval-Valued Intuitionistic Fuzzy Value IVIFN Interval-Valued Intuitionistic Fuzzy Number SS Schweizer-Sklar ATT Archimedean t-norm and t-conorm 4.2.2. Phase 2-Compute Weights for each QoS Attributes IVFS-SE Interval-Valued Intuitionistic Fuzzy Sets-Shannon Entropy DM Decision Maker
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Nivethitha Somu is an Institute Post Doctoral Fellow at Smart Energy Informatics Laboratory (SEIL), Department of Computer Science and Engineering, Indian Institute of Technology (IIT-B), Bombay. She was a Senior Research Fellow at Center for Information Super Highway (CISH) School of Computing, SASTRA Deemed University, Thanjavur, INDIA (2013–2018). She was awarded The Department of Science and Technology - ‘‘Innovation in Science Pursuit for Inspired Research (INSPIRE)’’ Fellowship’2013. She received her Master’s degree in Science from Anna University, Chennai, INDIA in 2011. She also received her Master’s degree in Technology from SASTRA Deemed University, Thanjavur, INDIA in 2013. She is a lifetime member of Ramanujan Mathematical Society. Her current research interests include Cloud service selection, QoS Prediction, Machine learning, Energy informatics, and Intrusion detection systems.
Obulaporam Gireesha is a Senior Research Fellow at Center for Information Super Highway (CISH) School of Computing, SASTRA Deemed University, Thanjavur, INDIA. She was awarded The Council for Scientific & Industrial Research (CSIR) - Senior Research Fellowship’ 2018. She obtained her Bachelor’s degree in Information Technology from Sri Padmavati Mahila VisvaVidyalayam (SPMVV) Women’s University, Tirupati, India in 2014. She received his Master’s degree in Software Engineering from Sree Vidyanikethan Engineering College (SVEC), Tirupati, India in 2016. She is a lifetime member of Ramanujan Mathematical Society. Her current research interests include Cloud service selection, Multi criteria decision making, and Elliptic curve cryptography.
Shankar Sriram V.S. is a Professor of Information Technology; and Chair Professor for TATA Communications — Cyber Security at School of Computing, SASTRA Deemed University, Thanjavur, Tamil Nadu, INDIA. He received his Bachelor’s degree in Science from Madurai Kamaraj University, Madurai, India. He obtained his Master’s degree in Computer Applications from Madurai Kamaraj University, Madurai, India. He also received his Master’s degree in Engineering from Thapar University, Punjab, India. He was conferred Ph.D. in Information and Network Security from Birla Institute of Technology, Mesra, India. He has been in the Academia for the past 19 years. He is a member of IEEE. He was awarded the IBM Shared University Research (SUR) Award’ 2017. His current area of research includes information and Network security, Cloud computing, Big data analytics, Machine learning, and Graph-based data mining.
Kannan Krithivasan is a Professor in the Department of Mathematics, SASTRA Deemed University, Thanjavur, INDIA. He obtained his Bachelor’s and Master’s degrees from the University of Madras, India, in 1980 and 1982, respectively. He also received his Bachelor’s and Master’s degrees in Education from Madurai Kamaraj University, India, in 1984 and 1986 respectively. He obtained his M.Phil. degree in Mathematics from Regional Engineering College, Tiruchirapalli, India, in 1988. He was conferred Ph.D. in Mathematics in the area of Computational Fluid Dynamics by Alagappa University, Karaikudi, India, in 2000. He is a member of IEEE. He is also a lifetime member of Ramanujan Mathematical Society. He has been in Academia for the past 34 years. His specific areas of interest include Combinatorial optimization, Hypergraph based image processing, and Bayesian computing.