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A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development
Computers & Industrial Engineering 132 (2019) 361–372
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A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development Elif Haktanıra,b, Cengiz Kahramana, a b
T
⁎
Istanbul Technical University, Department of Industrial Engineering, 34367 Macka, Besiktas, Istanbul, Turkey Altınbas University, Department of Industrial Engineering, 34217 Bagcilar, Istanbul, Turkey
ARTICLE INFO
ABSTRACT
Keywords: Pythagorean fuzzy sets QFD Photovoltaics Solar energy Product development
Quality function deployment (QFD) is a focused methodology for carefully listening to the voice of the customer and then effectively responding to those needs or customer requirements, (CRs) and expectations through design requirements (DRs). In classical QFD, exact numbers are used to determine the priorities of the CRs and the position of the company among the competitors. However, vagueness and impreciseness are inevitable uncertainties in those kinds of human evaluations, which are generally realized by linguistic terms. In this paper, the uncertainty in design processes is captured by a relatively new extension of ordinary fuzzy sets, Pythagorean fuzzy sets (PFS), aiming at presenting a larger domain to experts for assigning a membership degree and a nonmembership degree together with their hesitancy. We perform all the evaluation processes in the house of quality (HOQ) based on interval-valued PFS (IVPFS) and present some novel definitions for measuring and prioritizing CRs, DRs, and determining the position of the company among the competitors. We give an application of the proposed IVPF-HOQ model for solar photovoltaic technology development.
1. Introduction Both manufacturers and service providers must satisfy customer needs in the most extensive and perpetual way to survive in today’s extremely competitive business environment which obligates the companies to correspond to the dynamic and diversified CRs permanently and adapt themselves to the sectoral innovations to survive towards rivalries. The rapid changes in technology and increased customizations in product ranges impose lower production costs, shorter lead time, and higher product quality to be achieved in order to gain a sales and profit growth for sustaining competitive advantage in global markets. Modern world’s consumers have more expectancies and higher standards for a product than ever before. It is vital for the producers to sustain the balance between customer demands such as aesthetic concern, practical sufficiency, affordability and the engineering characteristic constraints like manufacturability, technological possibilities, functionalities, and cost. Since it is not possible to satisfy all customer demands in once, every company should decide on the priorities for each product or service they offer and regard those customer demands yet in the design phase. In the light of these facts, a useful product design and development technique to translate the customer needs to the product design specifications, named QFD, was developed in 1966, practiced by many ⁎
researchers in various cases and has become one of the most frequently applied methods for product development. Even QFD technique is often used in the design of products, some problems related to QFD analysis are reported in the literature. Iqbal, Grigg, Govindaraju, and Campbell-Allen (2016) defined correlation matrixes as roof matrixes that contain pairwise inter-correlations between DRs and divide the parts of HOQ into two as compulsory and optional. It is stated in their study that most of the researchers tend to ignore the optional parts of the HOQ presumably due to cost, time and evaluation difficulties concerns. It is also a major problem of those parts to integrate with the compulsory parts at the final absolute importance rankings of DRs. In this study, we take competitor analysis, correlation matrix and other parts into consideration since they all contain information that may affect the importance rankings of the DRs and misusage of them may cause inconvenient results. In our extent of knowledge from the literature review we conducted, correlation matrices of HOQ are often combined with theory of innovation problem solving (TRIZ) method (Shahin, Iraj, & Shahrestani, 2016; Zhang, Yang, & Liu, 2014) or to check the consistency (Shin, Kim, & Chandra, 2002). It is important to know the relations between DRs to reduce the duplication of effort if a positive relation exists between two DRs, which causes simultaneous satisfaction in both DRs when you enhance one; on the contrary if the correlation is negative, achievement of one may
Corresponding author. E-mail address: [email protected] (C. Kahraman).
https://doi.org/10.1016/j.cie.2019.04.022 Received 9 July 2018; Received in revised form 16 February 2019; Accepted 15 April 2019 Available online 26 April 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved.
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E. Haktanır and C. Kahraman
oppositely influence the other and lastly the third option is the low or zero relation which indicates mutually independence thus the necessity to satisfy the DRs on an individual basis to be able to meet entire CRs (Iqbal et al., 2016). Temponi, Yen, and Tiao (1999) divided the relationships between DRs into four: mutually exclusive, irrelevant, conflicting, or cooperative. If two DRs cannot be satisfied together even at some degree at the same time, they meant to be mutually exclusive and if satisfying one DR makes no difference on the other, it refers to irrelevant. To be conflicting, an increase in one DR should cause a decrease in the other one likewise if any decrease generates decrease on another DR they said to be cooperative. Customers generally define their expectations by using linguistic terms rather than exact or sharp numerical values such as very long life, high quality but quite cheap and very low noise. Similarly, the relations between customer needs and technical requirements are usually expressed by linguistic terms such as certainly high relation, low relation, and medium level relation. Besides, customer ratings and organizational difficulties can be expressed by linguistic terms such as high level satisfactory, low level satisfactory, very low difficulty, and certainly high difficulty. This causes a vagueness and impreciseness in these definitions. The methods in the literature for capturing this uncertainty are generally extended by fuzzy sets. Fuzzy sets are one of the most used tools for handling the uncertainty. Ordinary fuzzy sets have been extended to type-2 fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, and PFSs in the last two decades. In this paper, all these linguistic terms are represented by PFSs to give a larger domain for experts to assign membership and non-membership degrees. This is the superiority of PFS with respect to intuitionistic fuzzy sets. PFSs have not yet been used in the design of products. The originality of this paper is the first-time usage of PFSs in a QFD study and a comprehensive fuzzy approach to model the relations in HOQ. The rest of the paper is organized as follows. Section 2 presents a literature review on fuzzy QFD (FQFD). Section 3 gives the preliminaries for IVPFSs. Section 4 develops a novel IVPF-QFD Model. Section 5 illustrates the application of the proposed model on solar photovoltaic technology development. Section 6 concludes the paper with future directions.
manufacturing engineers and the last step, process control by the quality assurance department. Likewise, Zaim and Şevkli (2002) stated that QFD is a multidisciplinary process which needs to be done by diverse teams as marketing, design engineering, manufacturing engineering etc. QFD is a useful tool for both manufacturing and service sectors but it has mostly been applied in some specific sectors: software systems, manufacturing, transportation, supply chain, communication and service sectors (Abdolshah & Moradi, 2013; Çevik Onar, Büyüközkan, Öztayşi, & Kahraman, 2016). Within these sectors, it has mostly been imposed on the marketing, planning, product design, production and sales processes of the companies (Zaim & Şevkli, 2002). Wang, Lee, and Trappey (2017) developed the cloud-based production service concept for modeling a scalable and interoperable ordering system for self-service restaurants. They realized it through a structural and empirical service design using an integration of TRIZ, service QFD, and service blueprint approaches. He et al. (2017) proposed an improved Kano model named as importance-frequency Kano model and integrates it into QFD. The model adopts the logical Kano classification criteria to categorize CRs. Akkawuttiwanich and Yenradee (2018) proposed a new FQFD approach to manage the Supply Chain Operations Reference (SCOR) KPIs, which are widely used to measure supply chain performances by industrial practitioners. Jafarzadeh, Akbari, and Abedin (2018) proposed an integrated method which combines QFD, fuzzy logic, and data envelopment analysis. Babbar and Amin (2018) developed a novel QFD model to determine a set of suppliers and the order quantity. Their model is composed of a two-stage QFD and a stochastic multi-objective mathematical model. QFD usage provides various advantages to the companies such as highest level of customer satisfaction and better communication opportunities among multifunctional teams. Its usage causes an increase on product quality, process efficiency and company revenue vice versa a decrease on production cost and product designing time. The most common way to collect the CRs to build the HOQ and gather its inputs is to conduct surveys, interviews or focus group interviews with the customers, which can be experts, end-users or practitioners. Since these variables are mostly linguistic, they tend to be uncertain, imprecise, subjective, vague or fuzzy which may lead the results to be biased. Hence the conventional QFD is inadequate to overcome this problem, FQFD is developed by the researchers after L.A. Zadeh presented the fuzzy set theory in 1965. Classical QFD’s most common rate of importance scale is 1–5 crisp numbers, which usually causes a degree of information loss while FQFD uses linguistic variables that also might be imprecise or incomplete rather than crisp numbers that can be approximated to numerical precision and exactness under favor of fuzzy sets usage. There is a consensus in the literature for the effectiveness, reliability, accuracy and more meaningful results than classical QFD approaches that the FQFD brings. Liu (2011) classified the methods integrated with FQFD under more than nine titles as follows: conventional QFD computation using fuzzy variables, fuzzy outranking, entropy, fuzzy tendency analysis, fuzzy multi criteria decision making, fuzzy integral, fuzzy analytic network process, fuzzy expected value, fuzzy goal programming, fuzzy expert systems etc. Another classification of the models to develop FQFD is asserted by Abdolshah and Moradi (2013). They categorize the models into eight titles: fuzzy linear and nonlinear programming models, multicriteria decision making models, fuzzy group decision making models, metaheuristic methods, fuzzy regression models (linear and nonlinear), models proposed to prioritize CRs, hybrid models, and other methods. It is a necessity to make an accurate decision on which FQFD method to use for the success of the implementation. In most of the studies, triangular fuzzy numbers are used due to their easiness on computations rather than other types such as trapezoidal fuzzy numbers and LR fuzzy numbers (Abdolshah & Moradi, 2013). There are several other fuzzy extensions of QFD in the literature such as intuitionistic FQFD, neutrosophic QFD, and hesitant FQFD. To
2. Literature review on fuzzy QFD QFD can be described as a useful tool to translate CRs, needs or demands “or known as voice of customer” to the DRs, that is introduced in 1966 in Japan by Yoji Akao. It was utilized at Kobe Shipyards of Mitsubishi Heavy Industries in 1972 (Brief, 2012) and has been applied in many areas so far such as product design, quality management, decision making etc. (Sivasamy, Arumugam, Devadasan, Murugesh, & Thilak, 2016). It consists of four matrices that output of each matrix becomes the input of the next matrix. Four of the matrices are to represent the four phases of the processes: product planning, part deployment, process planning and product planning (Liu & Wang, 2010). The first matrix’s inputs (CRs) are being translated into the outputs as the DRs. The first matrix is also called as the HOQ matrix which is named by its shape that looks like a house with a roof. As it directly affects the next steps, the accuracy of this first matrix is vital for an accurate result at the end. HOQ is being built by gathering such components: CRs, DRs, priority ratings of each CRs, DRs’ correlation matrix and the relationship matrix between CRs and DRs which forms the body of the HOQ and shows the degree of each DRs’ effects on the related CRs. Abdolshah and Moradi (2013) revealed that majority of the companies and the research papers apply only the first phase of the QFD according to the time and cost concerns. Each step is better to be performed by the responsible departments in the firms. Brief (2012) proposed the product planning phase to be led by the marketing department, product design phase to be conducted by the engineering department, the process planning phase by 362
Computers & Industrial Engineering 132 (2019) 361–372
Inadequate to consider membership and non-membership functions together Data are received from another journal paper: Lee et al. (2017). The application depends on empirical analysis.
Inability to solve more complex problems in real life
make a comparison among these FQFD methods, Table 1 is presented. The advantages and disadvantages of these methods are included in Table 1 as well. Our proposed method is also compared with these existing methods. To gain a better understanding about the past studies on FQFD, a literature survey is conducted in this paper. Scopus is chosen as the main database to search for the related articles on FQFD. 231 document results are reached when the searching results are limited to the articles as the document type, journals as the source type, English as the language and QFD among other keywords. The analyses of searching results are given by graphical illustrations in the following. As shown in Fig. 1, the first article is published in 1997 on FQFD and the highest publication rate is reached in 2011 with 24 articles with the indicated specifications above. In Fig. 2, the subject areas that FQFD is applied are illustrated. They are engineering with 32%, computer science with 24%, decision sciences with 13%, business, management and accounting with 12%, mathematics with 9%, and others with 10%.
Opportunity to reflect customer requirements more comprehensively and accurately and offer highly detailed information for design teams Allocation of resources and coordinating skills based on customer needs, decreasing production costs, and reducing the cycle Ability to reflect the human’s hesitancy more objectively than the other classical extensions of fuzzy sets All the linguistic terms are represented by PFSs to give a larger domain for the assignment of membership and non-membership degrees and all the optional parts of an HOQ are considered.
Lack of effort to address the semantic in the linguistic variables No consideration of the relationship between the technical attributes and the degree of risk preference
3. Interval valued Pythagorean fuzzy sets Yager (2013) introduced PFSs and its basic set operations. Furthermore, Yager and Abbasov (2013) investigated the link between Pythagorean membership degrees and complex numbers. They develop a MCDM method involving Pythagorean fuzzy geometric mean and the order weighted geometric operator. Yager (2014) introduced aggregation operations for PFS. Zhang and Xu (2014) developed Pythagorean fuzzy TOPSIS. Peng and Yang (2015) defined division and subtraction operations and their properties for PFSs. Moreover, they introduced a Pythagorean fuzzy superiority and inferiority ranking method in order to tackle multiple attribute group decision making problems under uncertainty. Zhang (2016) proposed a closeness index-based ranking method for Pythagorean fuzzy numbers. Zhang, Li, and Ren (2016) discussed IVPFS and their basic operations. Then, they introduced Pythagorean fuzzy QUALIFLEX method to deal with MCDM problems. Dick, Yager, and Yazdanbakhsh (2016) studied complex valued membership grades by using PFS. Zhang et al. (2016) introduced Pythagorean fuzzy multi-granulation rough sets. Garg (2016) indicated the weakness of correlation coefficients between intuitionistic fuzzy sets and developed a new correlation coefficient and weighted correlation coefficient formulation between PFS. Garg (2017) proposed an improved accuracy function for the ranking order of IVPFS to eradicate the weakness of the current score and accuracy functions. Ilbahar, Karaşan, Cebi, and Kahraman (2018) developed an integrated methodology including Pythagorean fuzzy AHP and a fuzzy inference system and used it for risk assessment in the field of occupational health and safety. Yager (2013, 2014) introduced the PFS based on the idea that the sum of membership degree and non-membership degree may be larger than 1, but their square sum must be less than or equal 1.
Pythagorean FQFD
Definition 1. Let X be a fix set. A single-valued PFS P is an object having the form (Peng & Yang, 2016):
P = { x , (µp (x ), vp (x ) x
X },
(1)
[0, 1] defines the degree of membership and where the function µp : X vp: X [0, 1] defines the degree of non-membership of the element x X to P, respectively, and, for every x X , it holds that:
(µp (x )) 2 + (vp (x ))2
0
Çevik Onar et al. (2016) Authors of this paper
Hesitant FQFD
Green supplier evaluation and selection process Computer workstation selection Solar photovoltaic technology development Neutrosophic QFD Van et al. (2018)
Yu, Wang, and Bao (2018)
Intuitionistic FQFD
Simplification of the documentation process and computerization of QFD
Design requirements of a flexible manufacturing system Designing steering wheel of electric vehicles Khoo and Hot (1996)
Ordinary FQFD
Advantages Problem Area Type of FQFD Authors (Year)
Table 1 Comparison of FQFD methods.
Disadvantages
E. Haktanır and C. Kahraman
1.
(2)
The degree of hesitancy is given by Eq. (3): P (x )
or 363
=
1
(µp (x ))2
(vp (x )) 2 .
(3)
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E. Haktanır and C. Kahraman
30
25
20
15
10
5
0
Fig. 1. Frequencies of QFD publications over the years.
IVPFWG (A1 , A2 , A3 , k
=
Others, 19, 4%
Environmental Energy, 8, 2% Science, 10, 2%
i=1
where = ( 1, [0, 1] and i
Mathematics, 42, 9%
Decision Sciences, Computer Science, 112, 61, 13% 24%
(vp (x )) 2
(4)
A
2
B = ([ (µAL) + (µBL )2
µAU ],
(µAL )2 (µBL )2 ,
[vAL,
vAU ]
[µBL ,
2
U (µA ) + (µBU )
2
µBU ],
[vBL,
vBU ]
U µU ], [ (v L)2 + (v L)2 B = ([µAL µBL , µA B A B
(1
(µAL ) 2) ,
(A ) = ([(µAL ) , (µAU ) ], [ 1
1
2
2
(vAL) (vBL) ,
(1
(1
(
i
k
1
(1 i=1
2 i ( U A ) ) i
2
U ) + (vU ) (vA B
2
2
L 2 A) )
,
1
(1
(
U 2 A) )
])
,
is the weighted vector of Ai , i=1,2,…,k with = 1.
k i
=1
(µL2 + vL2 )
(10)
2 L
=1
(µU2 + vU2 )
(11)
(µL2 + µU2 + (1
vL2
2 U ) + (1
vU2
2 4 L ) + µL µU + (1
vL2
2 U)
(1
vU2
2 L) )
6
(12)
2
U ) (vU ) ]) (vA B
(µAU ) 2) ], [(vAL ) , (vAU ) ])
2, k i=1
)T
2 U
=
A larger value of PD (A ) indicates a larger A since 0 PD (A ) [0, 1].
(6)
A = ([ 1
i=1
( AL )2) i ,
PD (A )
U 2 U 2 U (µA ) (µB ) ], [vAL vBL, vU A vB ])
(5) A
(1
Definition 5. Let A = [µ L , µ U ], [v L, v U] be an IVPFN. The defuzzification of this number is calculated by Eq. (12). This defuzzification equation is based on dilation and concentration operations on membership and non-membership degrees.
Definition 2. Let A = ,B = be two IVPFNs, and > 0 , then the operations of these two IVPFNs are defined as follows (Peng & Yang, 2015):
[µAL ,
k
1
We know that the score functions or defuzzification functions are efficient when we compare PFNs in MADM problems. However, the score functions in the literature (Ren, Li, Chen, & Kuo, 2016; Zeng, Lin, Liu, & Sun, 2017), are insufficient to indicate which PFN is higher than the other since they don’t associate the hesitancy properly. Hence, we define a new defuzzification function as in Definition 5.
Fig. 2. FQFD subject areas.
(µp (x ))2
i=1
(µ Ai U ) i ,
Definition 4. Let A = [µ L , µ U ], [v L, v U] be an IVPFN, L and U are the hesitancy degree of the lower and upper points of A, respectively, can be calculated as in Eqs. (10) and (11):
Engineering, 148, 32%
Business, Management and Accounting, 53, 12%
=1
(µ Ai L) i ,
(9)
Social Sciences, 11, 2%
2 p (x )
, Ak ) k
µU2
+
vU2
1,
Definition 6. Let A = [µAL , µAU ], [vAL, vAU] and B = [µ BL , µ BU ], [v BL, v bU] be IVPFNs and LA , UA, LB and UB are the hesitancy degrees of lower and upper points of the A and B, respectively. The distance between A and B can be calculated as in Eq. (13) (Rahman et al., 2017):
(7) (8)
Definition 3. Let Ai , j=1,2,…,k be a collection of IVPFNs. Then, their aggregated value using IVPF Weighted Geometric (IVPFWG) operator is also an IVPFN satisfying (Rahman, Abdullah, Ahmed, & Ullah, 2017)
d (A, B ) =
364
2 ( (µAL 4
µBL )2 + (vAL
vBL ) 2 +
U (µA
µBU )2 + (vU A
vBU )2 )
(13)
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Table 2 Linguistic and corresponding numerical scale for the weights of criteria. Linguistic term
IVPF number
Certainly Low Importance (CLI)/Certainly Low Satisfactory (CLS)/Certainly Low Relation (CLR)/Certainly Low Difficulty (CLD) Very Low Importance (VLI)/Very Low Satisfactory (VLS)/Very Low Relation (VLR)/Very Low Difficulty (VLD) Low Importance (LI)/Low Satisfactory (LS)/Low Relation (LR)/Low Difficulty (LD) Medium Level Importance (MLI)/Medium Level Satisfactory (MLS)/Medium Level Relation (MLR)/Medium Level Difficulty (MLD) High Importance (HI)/High Satisfactory (HS)/High Relation (HR)/High Difficulty (HD) Very High Importance (VHI)/Very High Satisfactory (VHS)/Very High Relation (VHR)/Very High Difficulty (VHD) Certainly High Importance (CHI)/Certainly High Satisfactory (CHS)/Certainly High Relation (CHR)/Certainly High Difficulty (CHD)
([0.10,0.30],[0.70,0.90]) ([0.20,0.40],[0.60,0.80]) ([0.30,0.50],[0.50,0.70]) ([0.40,0.60],[0.40,0.60]) ([0.50,0.70],[0.30,0.50]) ([0.60,0.80],[0.20,0.40]) ([0.70,0.90],[0.10,0.30])
4. A novel IVPF-QFD model
color) with NC in the correlation matrix where PC means that the values of two DRs increase or decrease simultaneously by the change of the other. NC means that while the value of one DR increases, it causes the value of the other to decrease or vice versa. If there is no correlation, the cell is left empty which means alteration in one DR does not affect the other DR that we are investigating the relation with. In Fig. 7, each cell shows three assessments from three evaluators. If there are two fuzzy linguistic terms in one cell, it represents that only two experts state a correlation between those two DRs but not the third one. Step 6: Obtain the absolute importance ( AI ) for each DR by multiplying the aggregated linguistic importance evaluations (IE ) of CRs and the aggregated linguistic terms (R ) in the relationship matrix and the aggregated correlation impact factor (CI ) and then dividing by relative organizational difficulty (ROD) as in Eq. (14). The aggregated values of IE , R , and CI are obtained by using Eq. (3). Organizational difficulty (OD ) means how difficult it is for an organization to achieve a certain DR. The linguistic assessments for OD of each DR are aggregated before calculating (ROD ). Hence, we aim to decrease of the impact of DRs whose organizational difficulty is larger. Larger RODj values cause
In the following, we present the IVPF-QFD model based on the evaluations of three experts. If any of these experts has no opinion about the considered CRs or DRs, the opinions of the other experts are processed only. The proposed model is given by two phases and 12 steps as follows. Phase 1- CR&DR Relation Analysis Step 1: Define linguistic CRs and assign customer importance ratings by using Pythagorean fuzzy scale given in Table 2. This scale has been constructed by satisfying the conditions: systematic behavior, intersection between intervals, and replacement of membership and nonmembership intervals for reciprocal terms. CRs are rated by three experts as in Fig. 3 by using the scale in Table 2. Step 2: Define the DRs; determine the direction of improvement of DRs and fill in the relationship matrix as in Fig. 4. Step 3: Determine the level of organizational difficulty of the DRs by using the Pythagorean fuzzy scale given in Table 2 as in Fig. 5. Step 4: Determine the target values of DRs (How Muches) by using crisp numbers (α,β,…,η) in order to standardize the products as in Fig. 6. Step 5: Construct the correlation matrix among DRs as given in Fig. 7 by using the Pythagorean fuzzy scale given in Table 3. We denote positive correlation (blue color) with PC and negative correlation (red
smaller AIj . Relative absolute importance (RAI ) is obtained by Eq. (17). Arithmetic operations of IVPFSs must be considered while applying multiplication and addition. Division and subtraction operations for IVPFSs have not been explicitly defined in the literature. Hence, defuzzification is used whenever the subtraction and division operations are necessary in the following equations. Relative importance and absolute importance values are shown in HOQ in Fig. 8.
Fig. 3. CRs and linguistic customer importance ratings. 365
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E. Haktanır and C. Kahraman
Fig. 4. DRs, their direction of improvement and the relationship matrix. T=k+ i=1
AIij = {( h = 1, 2,
+l
IE i
Rhj )
, m , j = 1, 2,
, (r +
(1 + CIj )}
L , µ U ], [v L , v U ] RAj = [µ RA RA RA RA
(1 + RODj ),
j
where
CIj = (nc j (j
(pc ¯ j nc ¯ j)
(15)
r+ 1
1
+s
CIj
ODj
(16)
+1 and
CR
DO
Fuzzy relative absolute (RA) importance values are obtained by Eq. (17).
(
be an IVPFN and
L , RAj
U RAj
are the
Step 8: Determine the linguistic customer ratings of the competition by using the IVPF scale given in Table 2 as in Fig. 9. The linguistic customer ratings of the competition are assigned by multiple experts by using the scale in Table 2. To determine our position among the competitors, we first aggregate linguistic customer ratings with respect to the corresponding CR and then we measure the distances between our company and other CR companies (DO C ) using Eq. (18)
r and s: Numbers of sub-criterion under DR criteria groups k and l : Numbers of sub-criterion under CR criteria groups n cj : the number of correlations of DRj with the other DRs pc ¯ j : average of the positive correlations of DRj nc ¯ j : average of the negative correlations of DRj
RAij = AIij
j
Phase 2- Competitive Analysis
ODj
RODj = where
1))
j
hesitancy degree of lower and upper points of RAj , then the deffuzzifying procedure of this number calculated by Eq. (12). The highest RAj indicates the most important DR that the design engineers must take into account in the design phase of a new product.
(14)
+s)
j
r+ +s AIij ), j=1
i = 1, 2,
Step 7: Rank the DRs with respect to RAj
=
T=k+ t=1
+l
(
CR O C
CR
× dt
(O , C ) × IEt ),
= 1,
,y
(18)
where O and C represents our company and competitor , respectively. T represents the total number of sub-criteria of CRs. IEt is the aggregated linguistic customer ratings with respect to the corresponding CR. OCR C is defined as in Eq. (19)
(17)
,T
C
values. Let
Fig. 5. Organizational difficulty of the DRs. 366
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E. Haktanır and C. Kahraman
Fig. 6. Target values of DRs.
Fig. 7. Correlation matrix.
Table 3 IVPF correlation scale. Linguistic term for positive correlation
IVPF number
Linguistic term for negative correlation
Certainly Low Positive Correlation (CLPC) Very Low Positive Correlation (VLPC) Low Positive Correlation (LPC) Medium Level Positive Correlation (MLPC) High Positive Correlation (HPC) Very High Positive Correlation (VHPC) Certainly High Positive Correlation (CHPC)
([0.10,0.30],[0.70,0.90]) ([0.20,0.40],[0.60,0.80]) ([0.30,0.50],[0.50,0.70]) ([0.40,0.60],[0.40,0.60]) ([0.50,0.70],[0.30,0.50]) ([0.60,0.80],[0.20,0.40]) ([0.70,0.90],[0.10,0.30])
Certainly Low Negative Correlation (CLNC) Very Low Negative Correlation (VLNC) Low Negative Correlation (LNC) Medium Level Negative Correlation (MLNC) High Negative Correlation (HNC) Very High Negative Correlation (VHNC) Certainly High Negative Correlation (CHNC)
367
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Fig. 8. Relative importance and absolute importance values.
Fig. 9. Linguistic customer ratings of the competition. 368
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Fig. 10. Linguistic DR ratings of the competition.
CR O C
=
Company
+ 1, if O is better than Cl 1, if Cl is better than O 0, if O is equal to Cl
dtCR (O,
(19)
Fig. 11. Scale indicating the location of our company.
C ) is calculated by Eq. (20): 2 ( (µOL 4
dtCR (O, C ) =
(µOU
+
µClL )2 + (vOL U 2 µCl ) + (vOU
Company C1
vClL )2 U 2 vCl ) )
DR C
T=r+ t=1
=
+s
(
DR O C
× dt
DR
(O, C ) × AIij ),
= 1,
,y
=
+ 1, if O is better than Cl 1, if Cl is better than O 0, if O is equal to Cl
2 ( (µOL 4 +
(µOU
µClL ) 2 + (vOL U 2 µCl ) + (vOU
5. Application: solar photovoltaic technology development To demonstrate our proposed novel IVPF-QFD methodology, we select a case study given by Lee, Kang, Lin, and Chen (2017) that focuses on new product development for a photovoltaic (PV) solar cell manufacturer in Taiwan. The study claims that increasing environmental awareness and economical concerns directs more and more people to prefer solar energy. Nevertheless, the high cost and low conversion efficiency require producers to accomplish an active R&D study to overcome these issues. In their study, after the literature review, the authors carry out interviews with experts and the Taiwanese PV solar cell firm managers to list the possible CRs and DRs. Since it is not possible to list all the potential requirements, Fuzzy Delphi Method is applied to limit the list to the most important ones. Then, the prepared questionnaire is directed to the experts to weigh both CRs and DRs by their importance degrees correspondingly. After a series of calculations, by the answers of 6 experts, 12 CR candidates are narrowed down to the most important 6 ones while 16 DR candidates are reduced to 8. Their results indicate that the most important 6 CRs for a solar cell are as follows: conversion efficiency, manufacturing process, modular design, material quality, product stability, and government policy. The experts determine the following 8 DRs to meet the stated CRs: battery array density, antireflection film, velvet surface, quality control measures of cells, series elements in the module, pass of IEC 61215 and UL1703 standards, antireflection coated glass, and thermal expansion treatment. We applied these DRs and CRs to our case study in order to illustrate our proposed model. However, we slightly modified the DRs in Lee
(21)
(22)
vClL )2 U 2 vCl ) )
(23)
Step 10: Obtain the combined performance rating score (CPR ) of our company in order to determine our position among the competitors by considering both customer ratings and engineering assessments as in Eq. (24). CR
CPR = DO
C
(1
DR C
) DO
-0.0241
that our company is much worse than Cl .
dtDR (O , C ) is calculated by Eq. (23): dtDR (O , C ) =
0
Fig. 12. Relative position of our company.
where O and C represents our company and competitor , respectively. T represents the total number of sub-criteria of DRs. ODRC is defined as in Eq. (22). DR O C
Company C2
Our Company 0.0987
(20)
Step 9: Compare the DRs of our company with the other competitors by using the IVPF scale given in Table 2 as in Fig. 10. To determine our position among the competitors, we first aggregate linguistic engineering assessments with respect to the corresponding DR and then we measure the distances between our company DR and other companies (DO C ) using Eq. (21).
DO
Company
Our Company
(24)
) are the importance coefficients of CR and DR, where and (1 respectively. Step 11: Determine the relative position of our company on a scale as in the illustrative Fig. 11. Larger positive CPR indicates that our company is much better than Cl . Larger absolute negative CPR indicates 369
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E. Haktanır and C. Kahraman
VHPR MLPR HPR VHNR VHNR CLPR VLPR CLPR LPR LPR LPR
VHPR CHPR VHPR CHPR CHPR VHPR
CLNR CLNR LNR MLNR LNR
CLPR CLPR CLPR VLPR VLPR CLPR
MLPR MLPR MLNR MLNR MLNR
MLPR HPR HPR
CLNR CLNR VLNR
VHPR HPR HPR HNR HNR HNR
VLPR VLPR HPR MLPR MLPR
VHPR CHPR
VLPR CLPR LPR
HNR HNR MLNR
CHNR CHNR CHNR
Direction of Improvement HOWS
WHATS
Design Requirements
High conversion VHI, CHI, CHI efficiency Customer Requirements
Reflective film
Velvet surface
Quality control measures of cells
Series elements in the module
Pass of IEC 61215 and UL1703 standards
Reflective coated glass
Thermal expansion treatment
M LR LR LR
VLR LR M LR
CLR VLR CLR
LR VLR VLR
CLR CLR
CLR CLR CLR
M LR LR VLR
LR LR VLR
LR M LR
VLR VLR LR
VHR VHR VHR
Importance Evaluations
Subcriteria
Manufacturing process
VLR LR VLR
VLR VLR M LR
Modular design
LI, LI,LI
Material quality
MLI, LI, LI
Product stability
LI, VLI, LI
M LR HR M LR
LR LR LR VHR HR HR
CLR CLR VLR
VLR VLR VLR
VLR VLR VLR
CLR VLR VLR
VLR VLR CLR
MLS
O, C1, C2
O, O, C2
HS
O, C1
O, O, C1, C2
O, C1, C1, C2
O, C2, C2
O
O, C1, C1
O, C2, C2
O, C2
C1
HR HR
CLD,VLD, LD
LD, VLD, LD
M LD, M LD, LD
HD, M LD, VHD
M LD, VHD, HD
VLD, LD, CLD
CHD, CHD, VHD
How Muches
90 (Wh/Kg)
Relative transmission increase of 3.1% over the spectral range of 400–1100 nm
<5% reflection
100% In-line Inspection
72PV cells in series to charge 24V panel
Benchmark of 30% degradation
Increased transmission by up to 3.8%
20.3 (CTE) (10-6/K-1)
CLS
C1, C1
VLS
O, C1, C2
O, C1, C1, C2 O, C2
O, O, C1, C2, C2
C1
O , O , C2
O, C1, C1, C2
O, C1, C1, C2
C2
HS
C1, C2
O, O, O, C2, C2
VHS
O, O, C1, C1, C2
C1, C1, C1, C2
CHS
O, C2
VHS
CHS
O, O, C1, C2
C1, C2
C1
O, O, O, C1, C2
C1, C2, C2
O, C2
M LR HR LR
VHD, VHD, HD
MLS
LS
CHR CHR CHR
CLI, CLI, VLI
LS
VLS C1, C1
VHR VHR CHR
Organizational Difficulty
O: Our Company C1: Company 1 C2: Company 2
Customer Rating O: Our Company C1: Company 1 C2: Company 2 CLS
VHI, HI,MLI
Government policy
Engineering Assessment
Battery array density
O, C2
O, O, C2, C2 C1
O, C1, C2, C2
O, O, O, C1, C2
O, O, C1, C1,C2
Absolute Importance Relative Absolute Importance (%)
Fig. 13. Linguistic HOQ evaluated by three experts.
0.4932 0.6952 0.3131 0.5111 -0.6000 -0.8000 -0.2000 -0.4000 0.1260 0.3302
0.6316 0.8320
0.6707 0.8746 0.3000 0.5000
0.1735 0.3705 -0.1000 -0.3000
0.5000 0.7000
0.6649 0.8653
-0.7000 -0.9000
0.1418 0.3376
-0.3302 -0.5313
0.1000 0.3000
-0.1260 -0.3302
0.5313 0.7319
-0.4702 -0.6707
0.7000 0.9000
-0.6707 -0.8746
0.2713 0.4702
0.4000 0.6000
0.1587 0.3634
0.4000 0.6000
0.2000 0.4000
0.6377 0.8421
-0.5000 -0.7000
0.6000 0.8000
0.6481 0.8485
-0.3000 -0.5000
0.1585 0.3545
-0.4000 -0.6000
0.4642 0.6649
0.4309 0.6316
0.1817 0.3915
-0.4642 -0.6649
-0.7000 -0.9000
-0.4000 -0.6000
0.3376 0.5372
0.3705 0.5703
0.6119 0.8205
-0.3376 -0.5372
-0.1000 -0.3000
Design Requirements
HOWS Importance Evaluations WHATS
Battery array density
Reflective film
Velvet surface
Quality control measures of cells
Series elements in the module
Pass of IEC 61215 and UL1703 standards
Reflective coated glass
Thermal expansion treatment
Customer Requirements
Subcriteria High conversion efficiency
0.6649 0.8653 0.1418 0.3376 0.6649 0.8653 0.1418 0.3376 0.2884 0.4932 0.5111 0.7143 0.1260 0.3302 0.6707 0.8746 0.2289 0.4309 0.5703 0.7718 0.1000 0.3000 0.7000 0.9000 0.1000 0.3000 0.7000 0.9000 0.2884 0.4932 0.5111 0.7143 0.2621 0.4642 0.5372 0.7389
Manufacturing process
0.4932 0.6952 0.3131 0.5111
Modular design
0.3000 0.5000 0.5000 0.7000 0.2000 0.4000 0.6000 0.8000
Material quality
0.3302 0.5313 0.4702 0.6707
Product stability
0.2621 0.4642 0.5372 0.7389
0.5313 0.7319 0.2713 0.4702 0.2000 0.4000 0.6000 0.8000 0.1587 0.3634 0.6377 0.8421
Government policy
0.1260 0.3302 0.6707 0.8746
0.7000 0.9000 0.1000 0.3000
Organizational Difficulty
0.3464 0.5477 0.4542 0.6547 0.2289 0.4309 0.5703 0.7718 0.6000 0.8000 0.2000 0.4000 0.2289 0.4309 0.5703 0.7718 0.4309 0.6316 0.3705 0.5703 0.3000 0.5000 0.5000 0.7000
0.6316 0.8320 0.1735 0.3705
0.1260 0.3302 0.6707 0.8746 0.2000 0.4000 0.6000 0.8000 0.1587 0.3634 0.6377 0.8421 0.3915 0.5944 0.4114 0.6119 0.5000 0.7000 0.3000 0.5000
0.5646 0.7652 0.2387 0.4372 0.1817 0.3915 0.6119 0.8205 0.2621 0.4642 0.5372 0.7389 0.3634 0.5646 0.4372 0.6377 0.4932 0.6952 0.3131 0.5111 0.4932 0.6952 0.3131 0.5111 0.1817 0.3915 0.6119 0.8205 0.6649 0.8653 0.1418 0.3376
Defuzzified Organizational Difficulty
0.4830
0.1184
0.1731
0.2600
0.3969
0.3969
0.1184
Defuzzified Relative Organizational Difficulty
0.5257
0.1289
0.1884
0.2830
0.4321
0.4321
0.1289
0.6741
Absolute Importance
0.2945
0.1511
0.0739
0.1959
0.0880
0.1973
0.1485
0.1353
Relative Absolute Importance (%)
0.2292
0.1176
0.0576
0.1525
0.0685
0.1536
0.1156
0.1053
Fig. 14. Aggregated linguistic terms and corresponding IVPFSs. 370
0.6193
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E. Haktanır and C. Kahraman
producing products meeting those needs. The voice of customers is summarized in the HOQ, translating the needs into the technical characteristics. When assessments of the voice of customers are made by linguistic terms and by multiple experts, a fuzzy approach is needed together with an aggregation operator. After the introduction of intuitionistic fuzzy sets to the literature, PFSs have been proposed since they have a larger domain for the determination of membership and non-membership degrees. Our QFD study has been based on multi-expert linguistic assessments and these data have been processed by IVPFSs. Through the aggregation operators and IVPF operations, the relations among the elements of HOQ have been defined. Performance analysis of our company among competitors has been formulated by IVPFS. The proposed equations have successfully measured the absolute importance of the DRs and the distances between our company and the competitors. Our study aimed to set the relations in a HOQ in a comprehensive way under Pythagorean fuzziness. For further research, we suggest a comparative analysis through neutrosophic QFD analysis. Neutrosophic sets are based on a three-dimensional definition: truthiness, indeterminacy, and falsity corresponding to membership, hesitancy, and non-membership, respectively. The aggregation operations can be also developed by using q-rung orthopair fuzzy Heronian mean operators (Wei, Gao, & Wei, 2018), IVPF Maclaurin symmetric mean operators (Wei, Garg, Gao, & Wei, 2018), Pythagorean hesitant fuzzy Hamacher aggregation operators (Wei, Lu, Tang, & Wei, 2018), q-rung orthopair fuzzy Maclaurin symmetric mean operators (Wei, Wei, Wang, Gao, & Wei, 2019), q-rung interval-valued orthopair fuzzy Hamy mean operator (Wang, Gao, Wei, & Wei, 2019) to provide a comparison with this study.
Table 4 Indicators for the relative position of Our Company. Distance between O
Explanation
Cl
Positive Negative Zero
Our company is better than Cl Our company is worse than Cl Equal performance
Table 5 Distances between our company and competitors for CRs. CR
Defuzzified Distances
Sub-criteria
O-C1
O-C2
High conversion efficiency Manufacturing process Modular design Material quality Product stability Government policy
0.1320 −0.0237 −0.0268 0.0420 0.0250 0.0088
0.0271 −0.0597 −0.0133 0.0144 −0.0137 0.0000
TOTAL
0.1575
−0.0452
Table 6 Distances between our company and competitors for DRs. DR
Defuzzified Distances
Sub-criteria
O-C1
O-C2
Battery array density Reflective film Velvet surface Quality control measures of cells Series elements in the module Pass of IEC 61,215 and UL 1703 standards Reflective coated glass Thermal expansion treatment
−0.0290 0.0087 −0.0078 0.0220 0.0175 0.0079 0.0000 0.0210
−0.0072 0.0040 −0.0017 0.0000 −0.0018 0.0000 0.0036 0.0000
TOTAL
0.0402
−0.0031
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Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie
A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development Elif Haktanıra,b, Cengiz Kahramana, a b
T
⁎
Istanbul Technical University, Department of Industrial Engineering, 34367 Macka, Besiktas, Istanbul, Turkey Altınbas University, Department of Industrial Engineering, 34217 Bagcilar, Istanbul, Turkey
ARTICLE INFO
ABSTRACT
Keywords: Pythagorean fuzzy sets QFD Photovoltaics Solar energy Product development
Quality function deployment (QFD) is a focused methodology for carefully listening to the voice of the customer and then effectively responding to those needs or customer requirements, (CRs) and expectations through design requirements (DRs). In classical QFD, exact numbers are used to determine the priorities of the CRs and the position of the company among the competitors. However, vagueness and impreciseness are inevitable uncertainties in those kinds of human evaluations, which are generally realized by linguistic terms. In this paper, the uncertainty in design processes is captured by a relatively new extension of ordinary fuzzy sets, Pythagorean fuzzy sets (PFS), aiming at presenting a larger domain to experts for assigning a membership degree and a nonmembership degree together with their hesitancy. We perform all the evaluation processes in the house of quality (HOQ) based on interval-valued PFS (IVPFS) and present some novel definitions for measuring and prioritizing CRs, DRs, and determining the position of the company among the competitors. We give an application of the proposed IVPF-HOQ model for solar photovoltaic technology development.
1. Introduction Both manufacturers and service providers must satisfy customer needs in the most extensive and perpetual way to survive in today’s extremely competitive business environment which obligates the companies to correspond to the dynamic and diversified CRs permanently and adapt themselves to the sectoral innovations to survive towards rivalries. The rapid changes in technology and increased customizations in product ranges impose lower production costs, shorter lead time, and higher product quality to be achieved in order to gain a sales and profit growth for sustaining competitive advantage in global markets. Modern world’s consumers have more expectancies and higher standards for a product than ever before. It is vital for the producers to sustain the balance between customer demands such as aesthetic concern, practical sufficiency, affordability and the engineering characteristic constraints like manufacturability, technological possibilities, functionalities, and cost. Since it is not possible to satisfy all customer demands in once, every company should decide on the priorities for each product or service they offer and regard those customer demands yet in the design phase. In the light of these facts, a useful product design and development technique to translate the customer needs to the product design specifications, named QFD, was developed in 1966, practiced by many ⁎
researchers in various cases and has become one of the most frequently applied methods for product development. Even QFD technique is often used in the design of products, some problems related to QFD analysis are reported in the literature. Iqbal, Grigg, Govindaraju, and Campbell-Allen (2016) defined correlation matrixes as roof matrixes that contain pairwise inter-correlations between DRs and divide the parts of HOQ into two as compulsory and optional. It is stated in their study that most of the researchers tend to ignore the optional parts of the HOQ presumably due to cost, time and evaluation difficulties concerns. It is also a major problem of those parts to integrate with the compulsory parts at the final absolute importance rankings of DRs. In this study, we take competitor analysis, correlation matrix and other parts into consideration since they all contain information that may affect the importance rankings of the DRs and misusage of them may cause inconvenient results. In our extent of knowledge from the literature review we conducted, correlation matrices of HOQ are often combined with theory of innovation problem solving (TRIZ) method (Shahin, Iraj, & Shahrestani, 2016; Zhang, Yang, & Liu, 2014) or to check the consistency (Shin, Kim, & Chandra, 2002). It is important to know the relations between DRs to reduce the duplication of effort if a positive relation exists between two DRs, which causes simultaneous satisfaction in both DRs when you enhance one; on the contrary if the correlation is negative, achievement of one may
Corresponding author. E-mail address: [email protected] (C. Kahraman).
https://doi.org/10.1016/j.cie.2019.04.022 Received 9 July 2018; Received in revised form 16 February 2019; Accepted 15 April 2019 Available online 26 April 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved.
Computers & Industrial Engineering 132 (2019) 361–372
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oppositely influence the other and lastly the third option is the low or zero relation which indicates mutually independence thus the necessity to satisfy the DRs on an individual basis to be able to meet entire CRs (Iqbal et al., 2016). Temponi, Yen, and Tiao (1999) divided the relationships between DRs into four: mutually exclusive, irrelevant, conflicting, or cooperative. If two DRs cannot be satisfied together even at some degree at the same time, they meant to be mutually exclusive and if satisfying one DR makes no difference on the other, it refers to irrelevant. To be conflicting, an increase in one DR should cause a decrease in the other one likewise if any decrease generates decrease on another DR they said to be cooperative. Customers generally define their expectations by using linguistic terms rather than exact or sharp numerical values such as very long life, high quality but quite cheap and very low noise. Similarly, the relations between customer needs and technical requirements are usually expressed by linguistic terms such as certainly high relation, low relation, and medium level relation. Besides, customer ratings and organizational difficulties can be expressed by linguistic terms such as high level satisfactory, low level satisfactory, very low difficulty, and certainly high difficulty. This causes a vagueness and impreciseness in these definitions. The methods in the literature for capturing this uncertainty are generally extended by fuzzy sets. Fuzzy sets are one of the most used tools for handling the uncertainty. Ordinary fuzzy sets have been extended to type-2 fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, and PFSs in the last two decades. In this paper, all these linguistic terms are represented by PFSs to give a larger domain for experts to assign membership and non-membership degrees. This is the superiority of PFS with respect to intuitionistic fuzzy sets. PFSs have not yet been used in the design of products. The originality of this paper is the first-time usage of PFSs in a QFD study and a comprehensive fuzzy approach to model the relations in HOQ. The rest of the paper is organized as follows. Section 2 presents a literature review on fuzzy QFD (FQFD). Section 3 gives the preliminaries for IVPFSs. Section 4 develops a novel IVPF-QFD Model. Section 5 illustrates the application of the proposed model on solar photovoltaic technology development. Section 6 concludes the paper with future directions.
manufacturing engineers and the last step, process control by the quality assurance department. Likewise, Zaim and Şevkli (2002) stated that QFD is a multidisciplinary process which needs to be done by diverse teams as marketing, design engineering, manufacturing engineering etc. QFD is a useful tool for both manufacturing and service sectors but it has mostly been applied in some specific sectors: software systems, manufacturing, transportation, supply chain, communication and service sectors (Abdolshah & Moradi, 2013; Çevik Onar, Büyüközkan, Öztayşi, & Kahraman, 2016). Within these sectors, it has mostly been imposed on the marketing, planning, product design, production and sales processes of the companies (Zaim & Şevkli, 2002). Wang, Lee, and Trappey (2017) developed the cloud-based production service concept for modeling a scalable and interoperable ordering system for self-service restaurants. They realized it through a structural and empirical service design using an integration of TRIZ, service QFD, and service blueprint approaches. He et al. (2017) proposed an improved Kano model named as importance-frequency Kano model and integrates it into QFD. The model adopts the logical Kano classification criteria to categorize CRs. Akkawuttiwanich and Yenradee (2018) proposed a new FQFD approach to manage the Supply Chain Operations Reference (SCOR) KPIs, which are widely used to measure supply chain performances by industrial practitioners. Jafarzadeh, Akbari, and Abedin (2018) proposed an integrated method which combines QFD, fuzzy logic, and data envelopment analysis. Babbar and Amin (2018) developed a novel QFD model to determine a set of suppliers and the order quantity. Their model is composed of a two-stage QFD and a stochastic multi-objective mathematical model. QFD usage provides various advantages to the companies such as highest level of customer satisfaction and better communication opportunities among multifunctional teams. Its usage causes an increase on product quality, process efficiency and company revenue vice versa a decrease on production cost and product designing time. The most common way to collect the CRs to build the HOQ and gather its inputs is to conduct surveys, interviews or focus group interviews with the customers, which can be experts, end-users or practitioners. Since these variables are mostly linguistic, they tend to be uncertain, imprecise, subjective, vague or fuzzy which may lead the results to be biased. Hence the conventional QFD is inadequate to overcome this problem, FQFD is developed by the researchers after L.A. Zadeh presented the fuzzy set theory in 1965. Classical QFD’s most common rate of importance scale is 1–5 crisp numbers, which usually causes a degree of information loss while FQFD uses linguistic variables that also might be imprecise or incomplete rather than crisp numbers that can be approximated to numerical precision and exactness under favor of fuzzy sets usage. There is a consensus in the literature for the effectiveness, reliability, accuracy and more meaningful results than classical QFD approaches that the FQFD brings. Liu (2011) classified the methods integrated with FQFD under more than nine titles as follows: conventional QFD computation using fuzzy variables, fuzzy outranking, entropy, fuzzy tendency analysis, fuzzy multi criteria decision making, fuzzy integral, fuzzy analytic network process, fuzzy expected value, fuzzy goal programming, fuzzy expert systems etc. Another classification of the models to develop FQFD is asserted by Abdolshah and Moradi (2013). They categorize the models into eight titles: fuzzy linear and nonlinear programming models, multicriteria decision making models, fuzzy group decision making models, metaheuristic methods, fuzzy regression models (linear and nonlinear), models proposed to prioritize CRs, hybrid models, and other methods. It is a necessity to make an accurate decision on which FQFD method to use for the success of the implementation. In most of the studies, triangular fuzzy numbers are used due to their easiness on computations rather than other types such as trapezoidal fuzzy numbers and LR fuzzy numbers (Abdolshah & Moradi, 2013). There are several other fuzzy extensions of QFD in the literature such as intuitionistic FQFD, neutrosophic QFD, and hesitant FQFD. To
2. Literature review on fuzzy QFD QFD can be described as a useful tool to translate CRs, needs or demands “or known as voice of customer” to the DRs, that is introduced in 1966 in Japan by Yoji Akao. It was utilized at Kobe Shipyards of Mitsubishi Heavy Industries in 1972 (Brief, 2012) and has been applied in many areas so far such as product design, quality management, decision making etc. (Sivasamy, Arumugam, Devadasan, Murugesh, & Thilak, 2016). It consists of four matrices that output of each matrix becomes the input of the next matrix. Four of the matrices are to represent the four phases of the processes: product planning, part deployment, process planning and product planning (Liu & Wang, 2010). The first matrix’s inputs (CRs) are being translated into the outputs as the DRs. The first matrix is also called as the HOQ matrix which is named by its shape that looks like a house with a roof. As it directly affects the next steps, the accuracy of this first matrix is vital for an accurate result at the end. HOQ is being built by gathering such components: CRs, DRs, priority ratings of each CRs, DRs’ correlation matrix and the relationship matrix between CRs and DRs which forms the body of the HOQ and shows the degree of each DRs’ effects on the related CRs. Abdolshah and Moradi (2013) revealed that majority of the companies and the research papers apply only the first phase of the QFD according to the time and cost concerns. Each step is better to be performed by the responsible departments in the firms. Brief (2012) proposed the product planning phase to be led by the marketing department, product design phase to be conducted by the engineering department, the process planning phase by 362
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Inadequate to consider membership and non-membership functions together Data are received from another journal paper: Lee et al. (2017). The application depends on empirical analysis.
Inability to solve more complex problems in real life
make a comparison among these FQFD methods, Table 1 is presented. The advantages and disadvantages of these methods are included in Table 1 as well. Our proposed method is also compared with these existing methods. To gain a better understanding about the past studies on FQFD, a literature survey is conducted in this paper. Scopus is chosen as the main database to search for the related articles on FQFD. 231 document results are reached when the searching results are limited to the articles as the document type, journals as the source type, English as the language and QFD among other keywords. The analyses of searching results are given by graphical illustrations in the following. As shown in Fig. 1, the first article is published in 1997 on FQFD and the highest publication rate is reached in 2011 with 24 articles with the indicated specifications above. In Fig. 2, the subject areas that FQFD is applied are illustrated. They are engineering with 32%, computer science with 24%, decision sciences with 13%, business, management and accounting with 12%, mathematics with 9%, and others with 10%.
Opportunity to reflect customer requirements more comprehensively and accurately and offer highly detailed information for design teams Allocation of resources and coordinating skills based on customer needs, decreasing production costs, and reducing the cycle Ability to reflect the human’s hesitancy more objectively than the other classical extensions of fuzzy sets All the linguistic terms are represented by PFSs to give a larger domain for the assignment of membership and non-membership degrees and all the optional parts of an HOQ are considered.
Lack of effort to address the semantic in the linguistic variables No consideration of the relationship between the technical attributes and the degree of risk preference
3. Interval valued Pythagorean fuzzy sets Yager (2013) introduced PFSs and its basic set operations. Furthermore, Yager and Abbasov (2013) investigated the link between Pythagorean membership degrees and complex numbers. They develop a MCDM method involving Pythagorean fuzzy geometric mean and the order weighted geometric operator. Yager (2014) introduced aggregation operations for PFS. Zhang and Xu (2014) developed Pythagorean fuzzy TOPSIS. Peng and Yang (2015) defined division and subtraction operations and their properties for PFSs. Moreover, they introduced a Pythagorean fuzzy superiority and inferiority ranking method in order to tackle multiple attribute group decision making problems under uncertainty. Zhang (2016) proposed a closeness index-based ranking method for Pythagorean fuzzy numbers. Zhang, Li, and Ren (2016) discussed IVPFS and their basic operations. Then, they introduced Pythagorean fuzzy QUALIFLEX method to deal with MCDM problems. Dick, Yager, and Yazdanbakhsh (2016) studied complex valued membership grades by using PFS. Zhang et al. (2016) introduced Pythagorean fuzzy multi-granulation rough sets. Garg (2016) indicated the weakness of correlation coefficients between intuitionistic fuzzy sets and developed a new correlation coefficient and weighted correlation coefficient formulation between PFS. Garg (2017) proposed an improved accuracy function for the ranking order of IVPFS to eradicate the weakness of the current score and accuracy functions. Ilbahar, Karaşan, Cebi, and Kahraman (2018) developed an integrated methodology including Pythagorean fuzzy AHP and a fuzzy inference system and used it for risk assessment in the field of occupational health and safety. Yager (2013, 2014) introduced the PFS based on the idea that the sum of membership degree and non-membership degree may be larger than 1, but their square sum must be less than or equal 1.
Pythagorean FQFD
Definition 1. Let X be a fix set. A single-valued PFS P is an object having the form (Peng & Yang, 2016):
P = { x , (µp (x ), vp (x ) x
X },
(1)
[0, 1] defines the degree of membership and where the function µp : X vp: X [0, 1] defines the degree of non-membership of the element x X to P, respectively, and, for every x X , it holds that:
(µp (x )) 2 + (vp (x ))2
0
Çevik Onar et al. (2016) Authors of this paper
Hesitant FQFD
Green supplier evaluation and selection process Computer workstation selection Solar photovoltaic technology development Neutrosophic QFD Van et al. (2018)
Yu, Wang, and Bao (2018)
Intuitionistic FQFD
Simplification of the documentation process and computerization of QFD
Design requirements of a flexible manufacturing system Designing steering wheel of electric vehicles Khoo and Hot (1996)
Ordinary FQFD
Advantages Problem Area Type of FQFD Authors (Year)
Table 1 Comparison of FQFD methods.
Disadvantages
E. Haktanır and C. Kahraman
1.
(2)
The degree of hesitancy is given by Eq. (3): P (x )
or 363
=
1
(µp (x ))2
(vp (x )) 2 .
(3)
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30
25
20
15
10
5
0
Fig. 1. Frequencies of QFD publications over the years.
IVPFWG (A1 , A2 , A3 , k
=
Others, 19, 4%
Environmental Energy, 8, 2% Science, 10, 2%
i=1
where = ( 1, [0, 1] and i
Mathematics, 42, 9%
Decision Sciences, Computer Science, 112, 61, 13% 24%
(vp (x )) 2
(4)
A
2
B = ([ (µAL) + (µBL )2
µAU ],
(µAL )2 (µBL )2 ,
[vAL,
vAU ]
[µBL ,
2
U (µA ) + (µBU )
2
µBU ],
[vBL,
vBU ]
U µU ], [ (v L)2 + (v L)2 B = ([µAL µBL , µA B A B
(1
(µAL ) 2) ,
(A ) = ([(µAL ) , (µAU ) ], [ 1
1
2
2
(vAL) (vBL) ,
(1
(1
(
i
k
1
(1 i=1
2 i ( U A ) ) i
2
U ) + (vU ) (vA B
2
2
L 2 A) )
,
1
(1
(
U 2 A) )
])
,
is the weighted vector of Ai , i=1,2,…,k with = 1.
k i
=1
(µL2 + vL2 )
(10)
2 L
=1
(µU2 + vU2 )
(11)
(µL2 + µU2 + (1
vL2
2 U ) + (1
vU2
2 4 L ) + µL µU + (1
vL2
2 U)
(1
vU2
2 L) )
6
(12)
2
U ) (vU ) ]) (vA B
(µAU ) 2) ], [(vAL ) , (vAU ) ])
2, k i=1
)T
2 U
=
A larger value of PD (A ) indicates a larger A since 0 PD (A ) [0, 1].
(6)
A = ([ 1
i=1
( AL )2) i ,
PD (A )
U 2 U 2 U (µA ) (µB ) ], [vAL vBL, vU A vB ])
(5) A
(1
Definition 5. Let A = [µ L , µ U ], [v L, v U] be an IVPFN. The defuzzification of this number is calculated by Eq. (12). This defuzzification equation is based on dilation and concentration operations on membership and non-membership degrees.
Definition 2. Let A = ,B = be two IVPFNs, and > 0 , then the operations of these two IVPFNs are defined as follows (Peng & Yang, 2015):
[µAL ,
k
1
We know that the score functions or defuzzification functions are efficient when we compare PFNs in MADM problems. However, the score functions in the literature (Ren, Li, Chen, & Kuo, 2016; Zeng, Lin, Liu, & Sun, 2017), are insufficient to indicate which PFN is higher than the other since they don’t associate the hesitancy properly. Hence, we define a new defuzzification function as in Definition 5.
Fig. 2. FQFD subject areas.
(µp (x ))2
i=1
(µ Ai U ) i ,
Definition 4. Let A = [µ L , µ U ], [v L, v U] be an IVPFN, L and U are the hesitancy degree of the lower and upper points of A, respectively, can be calculated as in Eqs. (10) and (11):
Engineering, 148, 32%
Business, Management and Accounting, 53, 12%
=1
(µ Ai L) i ,
(9)
Social Sciences, 11, 2%
2 p (x )
, Ak ) k
µU2
+
vU2
1,
Definition 6. Let A = [µAL , µAU ], [vAL, vAU] and B = [µ BL , µ BU ], [v BL, v bU] be IVPFNs and LA , UA, LB and UB are the hesitancy degrees of lower and upper points of the A and B, respectively. The distance between A and B can be calculated as in Eq. (13) (Rahman et al., 2017):
(7) (8)
Definition 3. Let Ai , j=1,2,…,k be a collection of IVPFNs. Then, their aggregated value using IVPF Weighted Geometric (IVPFWG) operator is also an IVPFN satisfying (Rahman, Abdullah, Ahmed, & Ullah, 2017)
d (A, B ) =
364
2 ( (µAL 4
µBL )2 + (vAL
vBL ) 2 +
U (µA
µBU )2 + (vU A
vBU )2 )
(13)
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Table 2 Linguistic and corresponding numerical scale for the weights of criteria. Linguistic term
IVPF number
Certainly Low Importance (CLI)/Certainly Low Satisfactory (CLS)/Certainly Low Relation (CLR)/Certainly Low Difficulty (CLD) Very Low Importance (VLI)/Very Low Satisfactory (VLS)/Very Low Relation (VLR)/Very Low Difficulty (VLD) Low Importance (LI)/Low Satisfactory (LS)/Low Relation (LR)/Low Difficulty (LD) Medium Level Importance (MLI)/Medium Level Satisfactory (MLS)/Medium Level Relation (MLR)/Medium Level Difficulty (MLD) High Importance (HI)/High Satisfactory (HS)/High Relation (HR)/High Difficulty (HD) Very High Importance (VHI)/Very High Satisfactory (VHS)/Very High Relation (VHR)/Very High Difficulty (VHD) Certainly High Importance (CHI)/Certainly High Satisfactory (CHS)/Certainly High Relation (CHR)/Certainly High Difficulty (CHD)
([0.10,0.30],[0.70,0.90]) ([0.20,0.40],[0.60,0.80]) ([0.30,0.50],[0.50,0.70]) ([0.40,0.60],[0.40,0.60]) ([0.50,0.70],[0.30,0.50]) ([0.60,0.80],[0.20,0.40]) ([0.70,0.90],[0.10,0.30])
4. A novel IVPF-QFD model
color) with NC in the correlation matrix where PC means that the values of two DRs increase or decrease simultaneously by the change of the other. NC means that while the value of one DR increases, it causes the value of the other to decrease or vice versa. If there is no correlation, the cell is left empty which means alteration in one DR does not affect the other DR that we are investigating the relation with. In Fig. 7, each cell shows three assessments from three evaluators. If there are two fuzzy linguistic terms in one cell, it represents that only two experts state a correlation between those two DRs but not the third one. Step 6: Obtain the absolute importance ( AI ) for each DR by multiplying the aggregated linguistic importance evaluations (IE ) of CRs and the aggregated linguistic terms (R ) in the relationship matrix and the aggregated correlation impact factor (CI ) and then dividing by relative organizational difficulty (ROD) as in Eq. (14). The aggregated values of IE , R , and CI are obtained by using Eq. (3). Organizational difficulty (OD ) means how difficult it is for an organization to achieve a certain DR. The linguistic assessments for OD of each DR are aggregated before calculating (ROD ). Hence, we aim to decrease of the impact of DRs whose organizational difficulty is larger. Larger RODj values cause
In the following, we present the IVPF-QFD model based on the evaluations of three experts. If any of these experts has no opinion about the considered CRs or DRs, the opinions of the other experts are processed only. The proposed model is given by two phases and 12 steps as follows. Phase 1- CR&DR Relation Analysis Step 1: Define linguistic CRs and assign customer importance ratings by using Pythagorean fuzzy scale given in Table 2. This scale has been constructed by satisfying the conditions: systematic behavior, intersection between intervals, and replacement of membership and nonmembership intervals for reciprocal terms. CRs are rated by three experts as in Fig. 3 by using the scale in Table 2. Step 2: Define the DRs; determine the direction of improvement of DRs and fill in the relationship matrix as in Fig. 4. Step 3: Determine the level of organizational difficulty of the DRs by using the Pythagorean fuzzy scale given in Table 2 as in Fig. 5. Step 4: Determine the target values of DRs (How Muches) by using crisp numbers (α,β,…,η) in order to standardize the products as in Fig. 6. Step 5: Construct the correlation matrix among DRs as given in Fig. 7 by using the Pythagorean fuzzy scale given in Table 3. We denote positive correlation (blue color) with PC and negative correlation (red
smaller AIj . Relative absolute importance (RAI ) is obtained by Eq. (17). Arithmetic operations of IVPFSs must be considered while applying multiplication and addition. Division and subtraction operations for IVPFSs have not been explicitly defined in the literature. Hence, defuzzification is used whenever the subtraction and division operations are necessary in the following equations. Relative importance and absolute importance values are shown in HOQ in Fig. 8.
Fig. 3. CRs and linguistic customer importance ratings. 365
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Fig. 4. DRs, their direction of improvement and the relationship matrix. T=k+ i=1
AIij = {( h = 1, 2,
+l
IE i
Rhj )
, m , j = 1, 2,
, (r +
(1 + CIj )}
L , µ U ], [v L , v U ] RAj = [µ RA RA RA RA
(1 + RODj ),
j
where
CIj = (nc j (j
(pc ¯ j nc ¯ j)
(15)
r+ 1
1
+s
CIj
ODj
(16)
+1 and
CR
DO
Fuzzy relative absolute (RA) importance values are obtained by Eq. (17).
(
be an IVPFN and
L , RAj
U RAj
are the
Step 8: Determine the linguistic customer ratings of the competition by using the IVPF scale given in Table 2 as in Fig. 9. The linguistic customer ratings of the competition are assigned by multiple experts by using the scale in Table 2. To determine our position among the competitors, we first aggregate linguistic customer ratings with respect to the corresponding CR and then we measure the distances between our company and other CR companies (DO C ) using Eq. (18)
r and s: Numbers of sub-criterion under DR criteria groups k and l : Numbers of sub-criterion under CR criteria groups n cj : the number of correlations of DRj with the other DRs pc ¯ j : average of the positive correlations of DRj nc ¯ j : average of the negative correlations of DRj
RAij = AIij
j
Phase 2- Competitive Analysis
ODj
RODj = where
1))
j
hesitancy degree of lower and upper points of RAj , then the deffuzzifying procedure of this number calculated by Eq. (12). The highest RAj indicates the most important DR that the design engineers must take into account in the design phase of a new product.
(14)
+s)
j
r+ +s AIij ), j=1
i = 1, 2,
Step 7: Rank the DRs with respect to RAj
=
T=k+ t=1
+l
(
CR O C
CR
× dt
(O , C ) × IEt ),
= 1,
,y
(18)
where O and C represents our company and competitor , respectively. T represents the total number of sub-criteria of CRs. IEt is the aggregated linguistic customer ratings with respect to the corresponding CR. OCR C is defined as in Eq. (19)
(17)
,T
C
values. Let
Fig. 5. Organizational difficulty of the DRs. 366
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Fig. 6. Target values of DRs.
Fig. 7. Correlation matrix.
Table 3 IVPF correlation scale. Linguistic term for positive correlation
IVPF number
Linguistic term for negative correlation
Certainly Low Positive Correlation (CLPC) Very Low Positive Correlation (VLPC) Low Positive Correlation (LPC) Medium Level Positive Correlation (MLPC) High Positive Correlation (HPC) Very High Positive Correlation (VHPC) Certainly High Positive Correlation (CHPC)
([0.10,0.30],[0.70,0.90]) ([0.20,0.40],[0.60,0.80]) ([0.30,0.50],[0.50,0.70]) ([0.40,0.60],[0.40,0.60]) ([0.50,0.70],[0.30,0.50]) ([0.60,0.80],[0.20,0.40]) ([0.70,0.90],[0.10,0.30])
Certainly Low Negative Correlation (CLNC) Very Low Negative Correlation (VLNC) Low Negative Correlation (LNC) Medium Level Negative Correlation (MLNC) High Negative Correlation (HNC) Very High Negative Correlation (VHNC) Certainly High Negative Correlation (CHNC)
367
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Fig. 8. Relative importance and absolute importance values.
Fig. 9. Linguistic customer ratings of the competition. 368
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Fig. 10. Linguistic DR ratings of the competition.
CR O C
=
Company
+ 1, if O is better than Cl 1, if Cl is better than O 0, if O is equal to Cl
dtCR (O,
(19)
Fig. 11. Scale indicating the location of our company.
C ) is calculated by Eq. (20): 2 ( (µOL 4
dtCR (O, C ) =
(µOU
+
µClL )2 + (vOL U 2 µCl ) + (vOU
Company C1
vClL )2 U 2 vCl ) )
DR C
T=r+ t=1
=
+s
(
DR O C
× dt
DR
(O, C ) × AIij ),
= 1,
,y
=
+ 1, if O is better than Cl 1, if Cl is better than O 0, if O is equal to Cl
2 ( (µOL 4 +
(µOU
µClL ) 2 + (vOL U 2 µCl ) + (vOU
5. Application: solar photovoltaic technology development To demonstrate our proposed novel IVPF-QFD methodology, we select a case study given by Lee, Kang, Lin, and Chen (2017) that focuses on new product development for a photovoltaic (PV) solar cell manufacturer in Taiwan. The study claims that increasing environmental awareness and economical concerns directs more and more people to prefer solar energy. Nevertheless, the high cost and low conversion efficiency require producers to accomplish an active R&D study to overcome these issues. In their study, after the literature review, the authors carry out interviews with experts and the Taiwanese PV solar cell firm managers to list the possible CRs and DRs. Since it is not possible to list all the potential requirements, Fuzzy Delphi Method is applied to limit the list to the most important ones. Then, the prepared questionnaire is directed to the experts to weigh both CRs and DRs by their importance degrees correspondingly. After a series of calculations, by the answers of 6 experts, 12 CR candidates are narrowed down to the most important 6 ones while 16 DR candidates are reduced to 8. Their results indicate that the most important 6 CRs for a solar cell are as follows: conversion efficiency, manufacturing process, modular design, material quality, product stability, and government policy. The experts determine the following 8 DRs to meet the stated CRs: battery array density, antireflection film, velvet surface, quality control measures of cells, series elements in the module, pass of IEC 61215 and UL1703 standards, antireflection coated glass, and thermal expansion treatment. We applied these DRs and CRs to our case study in order to illustrate our proposed model. However, we slightly modified the DRs in Lee
(21)
(22)
vClL )2 U 2 vCl ) )
(23)
Step 10: Obtain the combined performance rating score (CPR ) of our company in order to determine our position among the competitors by considering both customer ratings and engineering assessments as in Eq. (24). CR
CPR = DO
C
(1
DR C
) DO
-0.0241
that our company is much worse than Cl .
dtDR (O , C ) is calculated by Eq. (23): dtDR (O , C ) =
0
Fig. 12. Relative position of our company.
where O and C represents our company and competitor , respectively. T represents the total number of sub-criteria of DRs. ODRC is defined as in Eq. (22). DR O C
Company C2
Our Company 0.0987
(20)
Step 9: Compare the DRs of our company with the other competitors by using the IVPF scale given in Table 2 as in Fig. 10. To determine our position among the competitors, we first aggregate linguistic engineering assessments with respect to the corresponding DR and then we measure the distances between our company DR and other companies (DO C ) using Eq. (21).
DO
Company
Our Company
(24)
) are the importance coefficients of CR and DR, where and (1 respectively. Step 11: Determine the relative position of our company on a scale as in the illustrative Fig. 11. Larger positive CPR indicates that our company is much better than Cl . Larger absolute negative CPR indicates 369
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VHPR MLPR HPR VHNR VHNR CLPR VLPR CLPR LPR LPR LPR
VHPR CHPR VHPR CHPR CHPR VHPR
CLNR CLNR LNR MLNR LNR
CLPR CLPR CLPR VLPR VLPR CLPR
MLPR MLPR MLNR MLNR MLNR
MLPR HPR HPR
CLNR CLNR VLNR
VHPR HPR HPR HNR HNR HNR
VLPR VLPR HPR MLPR MLPR
VHPR CHPR
VLPR CLPR LPR
HNR HNR MLNR
CHNR CHNR CHNR
Direction of Improvement HOWS
WHATS
Design Requirements
High conversion VHI, CHI, CHI efficiency Customer Requirements
Reflective film
Velvet surface
Quality control measures of cells
Series elements in the module
Pass of IEC 61215 and UL1703 standards
Reflective coated glass
Thermal expansion treatment
M LR LR LR
VLR LR M LR
CLR VLR CLR
LR VLR VLR
CLR CLR
CLR CLR CLR
M LR LR VLR
LR LR VLR
LR M LR
VLR VLR LR
VHR VHR VHR
Importance Evaluations
Subcriteria
Manufacturing process
VLR LR VLR
VLR VLR M LR
Modular design
LI, LI,LI
Material quality
MLI, LI, LI
Product stability
LI, VLI, LI
M LR HR M LR
LR LR LR VHR HR HR
CLR CLR VLR
VLR VLR VLR
VLR VLR VLR
CLR VLR VLR
VLR VLR CLR
MLS
O, C1, C2
O, O, C2
HS
O, C1
O, O, C1, C2
O, C1, C1, C2
O, C2, C2
O
O, C1, C1
O, C2, C2
O, C2
C1
HR HR
CLD,VLD, LD
LD, VLD, LD
M LD, M LD, LD
HD, M LD, VHD
M LD, VHD, HD
VLD, LD, CLD
CHD, CHD, VHD
How Muches
90 (Wh/Kg)
Relative transmission increase of 3.1% over the spectral range of 400–1100 nm
<5% reflection
100% In-line Inspection
72PV cells in series to charge 24V panel
Benchmark of 30% degradation
Increased transmission by up to 3.8%
20.3 (CTE) (10-6/K-1)
CLS
C1, C1
VLS
O, C1, C2
O, C1, C1, C2 O, C2
O, O, C1, C2, C2
C1
O , O , C2
O, C1, C1, C2
O, C1, C1, C2
C2
HS
C1, C2
O, O, O, C2, C2
VHS
O, O, C1, C1, C2
C1, C1, C1, C2
CHS
O, C2
VHS
CHS
O, O, C1, C2
C1, C2
C1
O, O, O, C1, C2
C1, C2, C2
O, C2
M LR HR LR
VHD, VHD, HD
MLS
LS
CHR CHR CHR
CLI, CLI, VLI
LS
VLS C1, C1
VHR VHR CHR
Organizational Difficulty
O: Our Company C1: Company 1 C2: Company 2
Customer Rating O: Our Company C1: Company 1 C2: Company 2 CLS
VHI, HI,MLI
Government policy
Engineering Assessment
Battery array density
O, C2
O, O, C2, C2 C1
O, C1, C2, C2
O, O, O, C1, C2
O, O, C1, C1,C2
Absolute Importance Relative Absolute Importance (%)
Fig. 13. Linguistic HOQ evaluated by three experts.
0.4932 0.6952 0.3131 0.5111 -0.6000 -0.8000 -0.2000 -0.4000 0.1260 0.3302
0.6316 0.8320
0.6707 0.8746 0.3000 0.5000
0.1735 0.3705 -0.1000 -0.3000
0.5000 0.7000
0.6649 0.8653
-0.7000 -0.9000
0.1418 0.3376
-0.3302 -0.5313
0.1000 0.3000
-0.1260 -0.3302
0.5313 0.7319
-0.4702 -0.6707
0.7000 0.9000
-0.6707 -0.8746
0.2713 0.4702
0.4000 0.6000
0.1587 0.3634
0.4000 0.6000
0.2000 0.4000
0.6377 0.8421
-0.5000 -0.7000
0.6000 0.8000
0.6481 0.8485
-0.3000 -0.5000
0.1585 0.3545
-0.4000 -0.6000
0.4642 0.6649
0.4309 0.6316
0.1817 0.3915
-0.4642 -0.6649
-0.7000 -0.9000
-0.4000 -0.6000
0.3376 0.5372
0.3705 0.5703
0.6119 0.8205
-0.3376 -0.5372
-0.1000 -0.3000
Design Requirements
HOWS Importance Evaluations WHATS
Battery array density
Reflective film
Velvet surface
Quality control measures of cells
Series elements in the module
Pass of IEC 61215 and UL1703 standards
Reflective coated glass
Thermal expansion treatment
Customer Requirements
Subcriteria High conversion efficiency
0.6649 0.8653 0.1418 0.3376 0.6649 0.8653 0.1418 0.3376 0.2884 0.4932 0.5111 0.7143 0.1260 0.3302 0.6707 0.8746 0.2289 0.4309 0.5703 0.7718 0.1000 0.3000 0.7000 0.9000 0.1000 0.3000 0.7000 0.9000 0.2884 0.4932 0.5111 0.7143 0.2621 0.4642 0.5372 0.7389
Manufacturing process
0.4932 0.6952 0.3131 0.5111
Modular design
0.3000 0.5000 0.5000 0.7000 0.2000 0.4000 0.6000 0.8000
Material quality
0.3302 0.5313 0.4702 0.6707
Product stability
0.2621 0.4642 0.5372 0.7389
0.5313 0.7319 0.2713 0.4702 0.2000 0.4000 0.6000 0.8000 0.1587 0.3634 0.6377 0.8421
Government policy
0.1260 0.3302 0.6707 0.8746
0.7000 0.9000 0.1000 0.3000
Organizational Difficulty
0.3464 0.5477 0.4542 0.6547 0.2289 0.4309 0.5703 0.7718 0.6000 0.8000 0.2000 0.4000 0.2289 0.4309 0.5703 0.7718 0.4309 0.6316 0.3705 0.5703 0.3000 0.5000 0.5000 0.7000
0.6316 0.8320 0.1735 0.3705
0.1260 0.3302 0.6707 0.8746 0.2000 0.4000 0.6000 0.8000 0.1587 0.3634 0.6377 0.8421 0.3915 0.5944 0.4114 0.6119 0.5000 0.7000 0.3000 0.5000
0.5646 0.7652 0.2387 0.4372 0.1817 0.3915 0.6119 0.8205 0.2621 0.4642 0.5372 0.7389 0.3634 0.5646 0.4372 0.6377 0.4932 0.6952 0.3131 0.5111 0.4932 0.6952 0.3131 0.5111 0.1817 0.3915 0.6119 0.8205 0.6649 0.8653 0.1418 0.3376
Defuzzified Organizational Difficulty
0.4830
0.1184
0.1731
0.2600
0.3969
0.3969
0.1184
Defuzzified Relative Organizational Difficulty
0.5257
0.1289
0.1884
0.2830
0.4321
0.4321
0.1289
0.6741
Absolute Importance
0.2945
0.1511
0.0739
0.1959
0.0880
0.1973
0.1485
0.1353
Relative Absolute Importance (%)
0.2292
0.1176
0.0576
0.1525
0.0685
0.1536
0.1156
0.1053
Fig. 14. Aggregated linguistic terms and corresponding IVPFSs. 370
0.6193
Computers & Industrial Engineering 132 (2019) 361–372
E. Haktanır and C. Kahraman
producing products meeting those needs. The voice of customers is summarized in the HOQ, translating the needs into the technical characteristics. When assessments of the voice of customers are made by linguistic terms and by multiple experts, a fuzzy approach is needed together with an aggregation operator. After the introduction of intuitionistic fuzzy sets to the literature, PFSs have been proposed since they have a larger domain for the determination of membership and non-membership degrees. Our QFD study has been based on multi-expert linguistic assessments and these data have been processed by IVPFSs. Through the aggregation operators and IVPF operations, the relations among the elements of HOQ have been defined. Performance analysis of our company among competitors has been formulated by IVPFS. The proposed equations have successfully measured the absolute importance of the DRs and the distances between our company and the competitors. Our study aimed to set the relations in a HOQ in a comprehensive way under Pythagorean fuzziness. For further research, we suggest a comparative analysis through neutrosophic QFD analysis. Neutrosophic sets are based on a three-dimensional definition: truthiness, indeterminacy, and falsity corresponding to membership, hesitancy, and non-membership, respectively. The aggregation operations can be also developed by using q-rung orthopair fuzzy Heronian mean operators (Wei, Gao, & Wei, 2018), IVPF Maclaurin symmetric mean operators (Wei, Garg, Gao, & Wei, 2018), Pythagorean hesitant fuzzy Hamacher aggregation operators (Wei, Lu, Tang, & Wei, 2018), q-rung orthopair fuzzy Maclaurin symmetric mean operators (Wei, Wei, Wang, Gao, & Wei, 2019), q-rung interval-valued orthopair fuzzy Hamy mean operator (Wang, Gao, Wei, & Wei, 2019) to provide a comparison with this study.
Table 4 Indicators for the relative position of Our Company. Distance between O
Explanation
Cl
Positive Negative Zero
Our company is better than Cl Our company is worse than Cl Equal performance
Table 5 Distances between our company and competitors for CRs. CR
Defuzzified Distances
Sub-criteria
O-C1
O-C2
High conversion efficiency Manufacturing process Modular design Material quality Product stability Government policy
0.1320 −0.0237 −0.0268 0.0420 0.0250 0.0088
0.0271 −0.0597 −0.0133 0.0144 −0.0137 0.0000
TOTAL
0.1575
−0.0452
Table 6 Distances between our company and competitors for DRs. DR
Defuzzified Distances
Sub-criteria
O-C1
O-C2
Battery array density Reflective film Velvet surface Quality control measures of cells Series elements in the module Pass of IEC 61,215 and UL 1703 standards Reflective coated glass Thermal expansion treatment
−0.0290 0.0087 −0.0078 0.0220 0.0175 0.0079 0.0000 0.0210
−0.0072 0.0040 −0.0017 0.0000 −0.0018 0.0000 0.0036 0.0000
TOTAL
0.0402
−0.0031
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