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Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory
Journal Pre-proof Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory Wenjie Wang, Guangdong Tian, Tongzhu Zhang, Fangyi Li, Amir M. Fathollahi-Fard, Danqi Wang, Noor H. Jabarullahg, Zhiwu Li PII:
S0959-6526(20)34768-5
DOI:
https://doi.org/10.1016/j.jclepro.2020.124724
Reference:
JCLP 124724
To appear in:
Journal of Cleaner Production
Received Date: 15 April 2020 Revised Date:
28 September 2020
Accepted Date: 16 October 2020
Please cite this article as: Wang W, Tian G, Zhang d T, Li F, Fathollahi-Fard AM, Wang D, Jabarullahg NH, Li Z, Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory, Journal of Cleaner Production, https://doi.org/10.1016/j.jclepro.2020.124724. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Elsevier Ltd. All rights reserved.
Credit author statement: Wenjie Wang: Wang Data curation, Writing-Original draft preparation. Guangdong Tian: Conceptualization, Methodology, Software. Tongzhu Zhang: Zhang Investigation and Data curation. Guangdong Tian, Tian, Fangyi Fangyi Li and Danqi Wang: Wang: Supervision.:: Amir Mohammad FathollahiFathollahi-Fard: Fard Software, Validation.: Noor H. Jabarrullah and Zhiwu Li: Writing-
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Reviewing and Editing.
Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory Wenjie Wang a,b, Guangdong Tian a,b,c,*, Tongzhu Zhang d, Fangyi Li a,b, Amir Mohammad Fathollahi-Fard e, Danqi Wang f,*, Noor H. Jabarrullahg, Zhiwu Li h,i
a. Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan, 250061, China b. National Demonstration Center for Experimental Mechanical Engineering Education, Shandong
of
University, Jinan 250061, China
China
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c. School of Computer and Communication Engineering, Liaoning Shihua University, Fushun 113001,
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d. Automotive Standardization Research Institute, China Automotive Technology and Research Center, Tianjin 300300, China
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e. Department of Electrical Engineering, École de Technologie Supérieure, 1100 Notre-Dame St. W.,
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Montréal, Canada
f. State Key Laboratory of Automobile Simulation and Control, Jilin University, Changchun 130025,
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China
g. Institute of Aviation Technology, University Kuala Lumpur, Selangor, Malaysia
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h. Institute of Systems Engineering, Macau University of Science and Technology, Taipa 999078, Macau, China
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i. School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China Corresponding authors: G. D. Tian ([email protected]), D. Q. Wang ([email protected])
Abstract: Design for disassembly (DFD) is an essential design technique to consider the disassembly and recyclability of a product at the initial design stage. An efficient DFD technique provides the disassembling and recycling easily. However, the recent trends of disassembling and recycling are to consider the aspects of environmental and social sustainability. Due to shortage of energy and deterioration of the ecological environment, the sustainable production is an active research topic to use the economic and social benefits as the evaluation standard of a design scheme as well as its environmental characteristics. This paper provides a new approach for DFD based on sustainability. In this regard, a hybrid multi-attribute decision making (MADM) method integrating the regret theory (RT) and the entropy weighting method is firstly developed. To implement the proposed approach, an eight-criterion evaluation system 1
of schemes based on sustainability including the factors of disassembly energy consumption, disassembly accessibility, fastener ratio, toxic material proportion, material recovery rate, disassembly expense, production and use noise, and waste emissions, is established. To better describe the fuzziness of human thinking and to avoid information loss/distortion during information aggregation phases, the evaluation information given by experts is presented by our proposed interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs). The weight vector of index structure is determined by the entropy weighting method under the fuzzy environment. The RT is employed to get the final order of alternatives by considering and
of
quantitating both the risk attitude and the regret attitude of experts. To show the
ro
applicability of this study, a case study including four kinds of refrigerator schemes, is conducted to validate the proposed method. An extensive comparison with other
-p
recent and state of the art methods along with a sensitivity analysis of 13 experiments,
re
is executed to verify effectiveness and reliability of the proposed I2LI-RT method. Finally, the experimental results show that: 1) disassembly accessibility (C2), fastener
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ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on the scheme selection of DFD based on sustainability as those
na
attributes carry relatively the larger weights; 2) our proposed method outperforms
ur
other recent and state of the art methods and 3) the chosen scheme A1 is the winner in the majority of the sensitivity analysis cases (10 out of 13). At last but not least, the
Jo
main finding is to furnish a systematic and efficient decision support tool for sustainable performance evaluation of product schemes of DFD.
Keywords: Sustainability, Scheme selection, Design for disassembly (DFD), Multi-attribute decision making (MADM), Interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs), Regret theory (RT)
2
Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory Wenjie Wang a,b, Guangdong Tian a,b,c,*, Tongzhu Zhang d, Fangyi Li a,b, Amir M. Fathollahi-Fard e, Danqi Wang f,*, Noor H. Jabarullahg, Zhiwu Li h,i
a. Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan, 250061, China b. National Demonstration Center for Experimental Mechanical Engineering Education, Shandong
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University, Jinan 250061, China
China
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c. School of Computer and Communication Engineering, Liaoning Shihua University, Fushun 113001,
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d. Automotive Standardization Research Institute, China Automotive Technology and Research Center, Tianjin 300300, China
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e. Department of Electrical Engineering, École de Technologie Supérieure, University of Quebec,
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1100 Notre-Dame St. W., Montréal, Canada f. State Key Laboratory of Automobile Simulation and Control, Jilin University, Changchun 130025,
na
China
g. Institute of Aviation Technology, University Kuala Lumpur, Selangor, Malaysia
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h. Institute of Systems Engineering, Macau University of Science and Technology, Taipa 999078, Macau, China
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i. School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China Corresponding authors: G. D. Tian ([email protected]), D. Q. Wang ([email protected])
Abstract: Design for disassembly (DFD) is an essential design technique to consider the disassembly and recyclability of a product at the initial design stage. An efficient DFD technique provides the disassembling and recycling easily. However, the recent trends of disassembling and recycling are to consider the aspects of environmental and social sustainability. Due to shortage of energy and deterioration of the ecological environment, the sustainable production is an active research topic to use the economic and social benefits as the evaluation standard of a design scheme as well as its environmental characteristics. This paper provides a new approach for DFD based on sustainability. In this regard, a hybrid multi-attribute decision making (MADM) method integrating the regret theory (RT) and the entropy weighting method is firstly developed. To implement the proposed approach, an eight-criterion evaluation system 1
of schemes based on sustainability including the factors of disassembly energy consumption, disassembly accessibility, fastener ratio, toxic material proportion, material recovery rate, disassembly expense, production and use noise, and waste emissions, is established. To better describe the fuzziness of human thinking and to avoid information loss/distortion during information aggregation phases, the evaluation information given by experts is presented by our proposed interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs). The weight vector of index structure is determined by the entropy weighting method under the fuzzy environment. The RT is employed to get the final order of alternatives by considering and
of
quantitating both the risk attitude and the regret attitude of experts. To show the
ro
applicability of this study, a case study including four kinds of refrigerator schemes, is conducted to validate the proposed method. An extensive comparison with other
-p
recent and state of the art methods along with a sensitivity analysis of 13 experiments,
re
is executed to verify effectiveness and reliability of the proposed I2LI-RT method. Finally, the experimental results show that: 1) disassembly accessibility (C2), fastener
lP
ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on the scheme selection of DFD based on sustainability as those
na
attributes carry relatively the larger weights; 2) our proposed method outperforms
ur
other recent and state of the art methods and 3) the chosen scheme A1 is the winner in the majority of the sensitivity analysis cases (10 out of 13). At last but not least, the
Jo
main finding is to furnish a systematic and efficient decision support tool for sustainable performance evaluation of product schemes of DFD.
Keywords: Sustainability, Scheme selection, Design for disassembly (DFD), Multi-attribute decision making (MADM), Interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs), Regret theory (RT)
1. Introduction Nowadays, the rise in quantity and categories of obsolete products together with their improper disposing methods leads to heavy environmental pollution and huge waste of natural resources. This motivates a great pressure on maintaining sustainable development goals (Fathollahi-Fard et al., 2019a). In the summit of the Group of Twenty (G20), sustainability in global economy comes to be one of the most essential issues. Under such circumstances, some manufacturers choose to provide products 2
with green features or to establish a green supply chain (Yu et al., 2016; Qu et al., 2019). Design for disassembly (DFD) is a widely accepted efficient product design technique to produce a product that will be easily dismantled at the end of its lifecycle and therefore, the DFD can facilitate the product recovery process. A well-considered scheme of DFD not only guarantees a high productivity and a low energy consumption in disassembly processes, but also promotes the healthy development of industry (Fu et al., 2019; Fathollahi-Fard et al., 2019b). It goes without saying that some serious environmental problems such as global warming, stratospheric ozone
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depletion, and waste collection etc., promote manufacturing enterprises to consider
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the impact of a product design scheme on the environment (Yu and Lee, 2018). These reasons make the scheme selection of DFD based on sustainability, challengeable. To
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meet the sustainable development goals, this study aims to evaluate a set of product
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schemes of DFD and to rank them based on the criteria of sustainability with the use of a hybrid multi-attribute decision making (MADM) method.
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Scheme selection of DFD is usually studied as an MADM topic. To address various MADM problems, evaluation criteria and assessment methods are developed
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and proposed in the literature (Tian et al., 2018a). Many factors/criteria can directly
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effect on the evaluation performance of DFD schemes. For example, disassembly time and disassembly cost during the disassembly process are two typical core criteria
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in scheme evaluation and have been well-studied in the literature (Tian et al., 2019). However, various criteria and their complex relationships, makes the evaluation process, challengeable. To achieve a better performance in the scheme selection of DFD based on sustainability dimensions, a comprehensive evaluation scheme system to consider the environmental indicators, is indispensable and highly needed. Generally, the MADM methods aim to find out the best alternative or to order the alternatives from a finite number of schemes based on the evaluation information provided by relevant experts (Zhang et al., 2019). Due to the complexity of the environment and the fuzziness of human thinking, evaluation information may be ambiguous and may have some fuzziness to some extensions. Experts prefer the expression of their attitudes by using words/sentences instead of real numbers. To this end, this paper proposes the interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs) whose membership degree and non-membership degree are both denoted via interval 2-tuple linguistic terms, to better describe the fuzziness of environment 3
and avoid information loss in aggregation phases. On the other hand, it should be noted that a few scholars have successfully tried to introduce the RT initially proposed by Bell (1982) to solve various MADM problems (Qu et al., 2018; Peng et al., 2017). To the best of our knowledge, the RT, which has been used in recent decision making studies and whose effectiveness has been confirmed in real applications, is rarely studied in the area of scheme selection of DFD. In addition, some details are ignored in those existing MADM methods for scheme selection of DFD, e.g., environmental characteristics which should be emphatically considered to achieve the sustainability. With regards to aforementioned challenges and contributions, this paper
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concentrates on a hybrid MADM method in the area of DFD scheme selection. The
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proposed hybrid method assists engineers in choosing the optimal scheme of DFD based on criteria of sustainability. Generally, this work is with the below four main
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contributions:
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1) We propose a hybrid MADM method abbreviated as I2LI-RT to assess the performance of DFD schemes based on sustainability in a fuzzy environment.
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The qualitative evaluation information is processed by the proposed I2LIFNs to better describe the fuzziness and ambiguity. The main advantage of the
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proposed method is to avoid information loss/distortion in information
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aggregation phases.
2) To evaluate the DFD schemes regarding the sustainability, some
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environmental indicators (i.e., toxic material proportion, material recovery rate, production noise and use noise, and waste emissions) are introduced and combined with disassembly indicators (i.e., disassembly energy consumption, disassembly accessibility, fastener ratio, and disassembly expense) to form an eight-criterion scheme evaluation system of DFD.
3) Schemes are ranked and the optimal scheme is determined through the well-accepted RT method. This method is rarely studied in the area of DFD scheme selection as far as we know. 4) The proposed MADM method furnishes a systematic and an efficient decision support tool for sustainable production to assess the performance of DFD schemes. The reminder of the paper is arranged as follows: Section 2 introduces a summary of the related works in this study area. Section 3 presents the proposed I2LI-RT method and its main steps. A refrigerator scheme evaluation example as a 4
real case study to show the applicability of our hybrid method, is presented in Section 4, followed by sensitivity analysis and a comparative study with other recent and state of the art methods. Finally, Section 5 concludes the results, findings and draws the future outlines.
Nomenclature Design for disassembly
MADM
Multi-attribute decision-making
RT
Regret theory
I2LIFSs
Interval 2-tuple linguistic intuitionistic fuzzy sets
I2LIFNs
Interval 2-tuple linguistic intuitionistic fuzzy numbers
G20
Group of twenty
FSs
Fuzzy sets
IFSs
Intuitionistic fuzzy sets
IVIFSs
Interval-valued intuitionistic fuzzy sets
IVLIFSs
Interval-valued linguistic intuitionistic fuzzy sets
IVLIFNs
Interval-valued linguistic intuitionistic fuzzy numbers
LCA
Life cycle assessment
DFA
Design for assembly
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na
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of
DFD
GC
Gray correlation Analytic hierarchy process
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AHP
TOPSIS
Technique for order preference by similarity to an ideal solution
ANP
Analytic network process
DOE
Design of experiment
LTS
Linguistic term set
T-WAA
2-tuple weighted arithmetic average operator
ST
An linguistic term set A linguistic term Symbolic translation Fuzzy number
/ /
Membership degree to number
/
Non-membership degree to number
/
Hesitation degree to number
of fuzzy set of fuzzy set
of fuzzy set 5
,
Hamming distance between two fuzzy sets
and
Entropy value about fuzzy set Utility function
∆
!
%#
Regret aversion coefficient
Entropy value of attribute C#
Weight of attribute C#
Membership degree utility value of alternative A under attribute
of
C#
Non-membership degree utility value of alternative A under
ℎ
#
+
#
A
- A
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+* #
Rejoice value of membership degree of alternative A with
respect to that of alternative A
under attribute C#
Regret value of membership degree of alternative A
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ℎ* #
Normal distribution function
respect to that of alternative A
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'(
attribute C#
under attribute C#
respect to that of alternative A
under attribute C#
Regret value of non-membership degree of alternative A with
respect to that of alternative A Weights vector to experts
Regret value of alternative A
under attribute C#
Rejoice value of alternative A
. A
Comprehensive perception value of alternative A
23
Distance closeness index of alternative A
/0 A 1
.0 A
with
Rejoice value of non-membership degree of alternative A with
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%#
,
Regret-rejoice function
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$
!
Risk aversion coefficient
Amount of determinate information of alternative A GC closeness index of alternative A
Comprehensive perception value of alternative A
in the
comparison experiment
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2. Literature review Since the contributions of this paper are four points as discussed in the introduction, the literature review is divided into four different but related streams including DFD, MADM methods, fuzzy theories and RT. Finally, the research gaps have been identified and our contributions to fill them are discussed. 2.1. DFD Contrary to the traditional design methods, the DFD is an efficient design
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technique from the point of disassembly (Pan et al., 2001) and presents a remarkable application prospect. It is even regarded as a critical twenty-first century discipline
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that highlight a series of design rules (Bogue 2007).
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The idea of DFD has been used in various aspects in our daily life. For example,
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regarding the study of Kondo et al. (2004), the DFD strategy was implemented in the life cycle assessment (LCA) for end-of-life electric home appliances. Regarding the
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importance of disassemblability design for end-of-life products, Viswanathan et al. (2006) described a model to research on the combinatorial configuration design
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optimization problem with DFD technique. More recently, Favi et al. (2019)
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developed a time-based method and a software tool called Lean-DFD to assess the disassemblability of mechatronic products. To quantify the impacts of DFD on
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buildings, Denis et al. (2018) put forward a new method called disassembly network analysis and their experimental results demonstrate its promising prospect. As one of important study in the literature review, Bogue (2007) pointed out that a successful DFD should entail three essential principles including the choice and adoption of raw materials, the design of product architecture, and the selection and the use of joints/fasteners. To assist engineers for determining appropriate fasteners of DFD, Ghazilla et al. (2014) presented a multi-criterion decision-making model by utilizing PROMETHEE method. Aguiar et al. (2017) developed a diagnostic tool to assess product recyclability during the product design phase where the amount, type and accessibility of fasteners and other factors were considered. To have one more step, an active disassembling fastener, as a DFD technology, was used in a LCA of end-of-life appliances recycling system on the basis of the waste input-output model (Nakamura et al., 2010). In recent researches on the DFD, the idea of design for assembly (DFA) is 7
considered. Soh et al. (2016) proposed a hybrid and systematic methodology that incorporated DFD and DFA and restrained it from the remanufacturing perspective. Based on rating factors, Shetty et al. (2015) presented a novel design tool for DFD/DFA to effectively test the ease of disassembly/assembly of products as a recent topic in the area of DFD techniques. 2.2. MADM methods Recently, there is a great deal of attention in the application of MADM methods for the scheme evaluation/selection related to the decision-making fields, such as gray
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correlation (GC), analytic hierarchy process (AHP), technique for order preference by similarity to an ideal solution (TOPSIS), analytic network process (ANP), SAW,
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VIKOR and so on (Tian et al., 2018b).
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Although there are many MADM methods and each of them has a unique advantage, the hybrid MADM methods are recently proposed. For example, a group
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of MADM methods including SAW, TOPSIS, and VIKOR, was used and
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compounded to assess the safety of seven Iranian airlines (Barak et al., 2018). Based on Delphi method, Hsu et al. (2017) used a hybrid MADM method integrating the
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fuzzy AHP and the TOPSIS method to find key performances factors regarding the sustainability development of medium-sized enterprises. In addition, a new hybrid
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MADM model integrating ANP, DEMATEL-based ANP and GC method, was
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established to select optimal suppliers for addressing the supply chain management problem (Liou et al., 2016). Another new hybrid MADM technique consisting of ANP, TOPSIS and fuzzy max-min set methods, was introduced to assess several water transfer projects (Toosi et al., 2014). Most importantly, the hybrid MADM methods have been applied to disassembly evaluation field for product design, product recycle and so on (Feng et al., 2019a). For example, Yuan et al. (2019) used the GC technology to make a comprehensive evaluation of disassembly processes. Zhang et al. (2018) employed the AHP method on the basis of experts’ preferences for evaluating dismantling modes. Sabaghi et al. (2016) proposed a unique discriminant disassembly model to obtain disassemble ability index with the TOPSIS method and the design of experiment (DOE) method. As mentioned earlier, evaluation criteria are essential to the scheme selection of DFD and the hybrid MADM methods are needed. In this regard, Tang et al. (2004) offered a disassembly process evaluation model based on economic factors. On the 8
basis of Tang’s research, an environmental consequences criterion was added in Peeters et al. (2017) for an active disassembly evaluation. Recently, a five-criterion disassembly operation evaluation system including visibility, disassembly angle, number of tool’s changes and so on, was developed by Wang et al. (2016) with a software package designed by using Python programming language. Feng et al. (2019c) introduced three green indices of disassembly, i.e., disassembly cost, number of toxic parts and materials compatibility to determine a best scheme. At last but not least, the disassembly operation comport was selected as an evaluation index for product maintainability design (Zhu et al., 2020).
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2.3. Fuzzy theories
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Fuzziness is common in the literature review and can be encountered during the
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process of evaluating schemes of DFD. As one of important studies in the area of DFD, Tian et al. (2012) realized the quantitative evaluation for disassembly processes
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through stochastic linear programming and maximum entropy theory. In another
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different research, Tian et al. (2018c) focused on fuzzy component quality and process cost to optimize disassembly sequences. With the perspective of disassembly,
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Kazancoglu et al. (2018) utilized a fuzzy AHP approach to decide the criteria weights and employed a multi-objective optimization method to order disassembly tasks in
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addressing the disassembly line balancing problem under fuzzy environment.
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During the process of scheme selection in fuzzy environment, evaluation information on alternatives may be ambiguous and may have some fuzziness to some extent due to the complicacy of environments and the illegibility in human thinking, which is not suitable to be represented by exact numbers. For better expressing the uncertainty and fuzziness of information, several fuzzy theories are introduced, for example, fuzzy sets (FSs) (Zadeh 1965), intuitionistic fuzzy sets (IFSs) (Atanassov 1986) and interval-valued intuitionistic fuzzy sets (IVIFSs) (Atanassov et al., 1989). Compared with FSs, for IFSs, concepts of the membership degree and non-membership degree are added simultaneously and expressed in the form of crisp numbers. Different from IFSs, the membership degree and non-membership degree in IVIFSs are both denoted in the form of interval numbers instead of single crisp numbers, which is more expressive in describing uncertainty and fuzziness of evaluation information (Yang et al., 2020). However, the utilization of FSs, IFSs and IVIFSs may lead to the loss and distortion of information. According to Liu et al. 9
(2019), it will be more reasonable and convenient for experts to give their preference information by using linguistic forms sometimes. Later, Liu et al. (2017) put forward the concept of interval-valued linguistic intuitionistic fuzzy sets (IVLIFSs) which integrate the idea of linguistic variables and IVIFSs. As for IVLIFSs, membership degree and non-membership degree are both denoted by interval-valued linguistic terms to process imprecise information. However, although IVLIFSs can well address fuzziness under fuzzy environment, information loss may also occur in aggregation phases, which will mislead the evaluation results. The 2-tuple method proposed in Herrera et al. (2000), which can avoid information loss/distortion in information
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aggregation phases, is suitable for processing information with linguistic forms.
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2.4. RT
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Although the RT proposed by Bell (1982) is an old theory, it is rarely studied in the area of MADM models. For example, Wang et al. (2020) proposed a
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projection-based RT method for MADM problems under fuzzy sets environment.
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Gong at al. (2019) extended RT and applied it into the application for the stock market. The effectiveness of RT has been confirmed in real applications (Zhang et al., 2016).
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Peng et al. (2019) combined RT with ELECTRE III method to establish a model that could effectively support the decision-making of new energy investment. Its basic
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idea is that, the decision makers not only focus on the results of the scheme that they
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choose, but also pay attention to the comparison results between the scheme and other schemes that they do not choose in the decision making process, and avoid choosing the alternative that will make them feel regret (Qu et al., 2018; Peng et al., 2017). RT has the following three core characteristics: 1) it considers both the risk attitude and the regret attitude of decision makers; 2) it quantifies the psychological emotions of regret/rejoice of decision makers; 3) it involves few parameters and its calculation process is easy to understand. However, the adoption of RT is limited in scheme selection of DFD based on sustainability. As can be seen from the literature review, although there are many effective approaches to deal with the problem of scheme selection of DFD. Nevertheless, some aspects still be overlooked, e.g., environmental indicators, which have a significant impact on the assessment process for sustainable product design schemes, are rarely considered; RT, which has been successfully applied in recent decision making studies is limited to the evaluation of schemes of DFD. Besides, due to the complexity of the 10
environment and the fuzziness of human thinking, evaluation information may have some fuzziness to some extent and information loss may occur in aggregation phases. Therefore, the concept of interval 2-tuple linguistic intuitionistic fuzzy numbers is proposed and employed to present evaluation information. In this work, we will establish a comprehensive evaluation system of schemes of DFD based on sustainability in which disassembly and environmental characteristics of an alternative scheme are both considered. The weights vector of index structure is determined by the entropy weighting method. RT is utilized to obtain the final ranking
A hybrid MADM method I2LI-RT
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3.
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of schemes of DFD to select the most sustainable one.
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3.1. Interval 2-tuple linguistic intuitionistic fuzzy sets/numbers (I2LIFSs/I2LIFNs)
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Definition 3.1. Suppose X={x1, x2, …, xn}be the finite and nonempty universe of discourse. An interval 2-tuple linguistic intuitionistic fuzzy set (I2LIFS) is defined as:
2) J :;
,
D C
E
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E
= AB
,
D C
E
F,B
D C
E
,
D C
G C
E
,
D C
E
and 4) 0 ≤ ∆IS B
,
G C
G C
E
E
,
:;
,
E
G C
of set 45, which satisfy: 1)
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degree to
:;
D C
:;
,
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of set 45,
= AB
ur
:;
where
45 = 7<
E
F,B
,
I :;
G C
G C
E
E
,
>|
,
FH is the membership degree to G C
J :;
∈ N−0.5, 0.5 ; 3) G C
E
F + ∆IS B
∈ ?@
G C
E
E
,
,
FH is the non-membership ,
I :;
I :;
G C
E
≤
∈ 70,1, ⋯ , %@;
J :;
J :;
,
≤
I :;
F ≤ %. ST={s0, s1, ⋯,
st} is an linguistic term set (LTS) that is made up of a group of linguistic terms
(Herrera et al., 2000). ∆IS
that converts a 2-tuple to its equivalent numerical
al.,
degree
45
value is defined in Herrera et al. (2000). Similar to the definition of IVLIFNs (Liu et :;
2017), = AB
∆ U% − ∆IS B ∆ U% − ∆IS B
the D C
G C D C
E
E E
,
, ,
hesitation D C
G C D C
E
E E
F,B
G C
E
F − ∆IS B F − ∆IS B
,
G C D C
to G C
E E
E
, ,
FH
G C D C
of , E E
FV
FV.
set where ,
is
B B
expressed D C G C
E E
, ,
D C G C
E E
as
F= F=
Specially, if there exists only one element in set 45, then 45 degenerates into an 11
interval 2-tuple linguistic intuitionistic fuzzy number (I2LIFN) denoted simply as :; , :;
= BAB
D C
,
D C
F,B S,
Definition 3.2. Let X ={
YBAB
D C
E
,
D C
E
F,B
G C
E
YBAB
D ]
E
,
D ]
E
F,B
G ]
E
and
\; =
G C
X,
,
⋯,
G C
FH , AB
G C
E
FH , AB
,
G ]
E
FH , AB
,
G C
∆IS B ∆IS B
∆IS B S̃
̃ X
E
G C
E
G ]
,
G C
,
D C
E
,
G C
E
,
E
= N
= N
G ]
,
g , −0.3
E
E
F,
G C
d ( r%1, r%2 ) =
D ]
E
,
G C
E
D ]
the
D C
E
,
D C
D C
E
F,B
G C
E
,
G C
E
FHF Z
∈ ?[
D ]
E
,
D ]
E
F,B
G ]
E
,
G ]
E
FHF Z
∈ ?[
−
F,
E
e, N
−
^ , −0.5
G C
G ]
E
E
D ]
E
,
G ]
E
e, N
D ]
E
E
G C
E
,
D ]
F,
S , −0.5
S , 0.1
between sets 45 and \; is
G ]
E
Z+Z
= ∆IS B G ]
D ]
D C
E
,
E
E
D ]
,
,
G ]
E
,
Z+Z
D C
E
X , 0.2
G C
D ]
E
E
E
D ]
G ]
F
,
E
E
D C
−
E
G ]
D ]
D ]
E
−
D ]
F ,
G ]
F − ∆IS B
F.
between
F
E
E
D C
E
two
E
Z+ (1)
F,
,
,
D ]
ZF
E
E
= % − ∆IS B
E
distance
e
G ]
= ∆IS B
E
= ∆IS B
F − ∆IS B
,
E
= ∆IS B
= % − ∆IS B
f , 0.3
G C
45, \;
ro
D C
FHF.
E
Z+Z
hamming
G C
D C
=
E
=
E
,
D C
,
,
E
G ]
=%−
E
D C
E
F−
F,
I2LIFNs and
e is calculated by:
4 − 2.7 + 5.3 − 3.5 + 0.3 −1.1 + 0.5 − 2.2 + 0.2 − 0.3 + 1.7 − 2.2 = 0.258 4× 6
Definition 3.3. Let ? = 7 S ,
YBAB
Z+Z
F ,
E
F − ∆IS B
c , 0.3
,
E
G C
D C
-p
,
D ]
,
,
G C
example,
^, 0
E
E
,
F
= % − ∆IS B
For
G ]
D C
Jo
E
F
= ∆IS B
E
= ∆IS B
E
G ]
D C
E
−
ur
G C
E
E
−
,
,
lP
∆IS B
G C
E
na
D C
where
Z
D C
G C
E
re
S 45, \; = ^(_ ∑(aS BZ
F,B
D C
be the two I2LIFSs, the hamming distance
defined by:
D C
be the universe of discourse and 45 =
(}
,
D C
of
W=
E
F,B
G C
E
,
X, ⋯ , (@
G C
E
FH , AB
be the universe of discourse and 45 = D C
E
,
D C
F,B
E
be an I2LIFS. The entropy value of set 45 is expressed as: S 45 = ^(_ i ∑(aS 2% X − Z
G C
E
−
G C
E
X
Z −Z
D C
E
−
G C
D C
E
E
,
G C
X
E
Z +B
FHF Z D C
E
∈ ?[
X
F + 12
B
BAB
G C
E
F
X
(2)
Assuming that there are a group of I2LIFNs of size n, denoted as W = D k j
,
D k j
F,B
G k j
,
G k j
FH , AB
D k j
,
D k j
F,B
G k j
,
G k j
FHF, and their weights are marked
in vector l = mS , mX , ⋯ , m( n , then we aggregate them by using T-WAA operator defined in Herrera et al. (2000). The aggregation result is shown as:
D p j G p j
,
, ,
D p j G p j D p j G p j
G p j
,
G p j
FH , A
D p j
,
(
= ∆ uv m ∆IS B aS (
F = ∆ uv m ∆IS B
D p j
D k j
,
,B D k j
G p j
,
G p j
FHF
(3)
Fw
of
G p j
,
,B
G k j
,
G k j
Fw
ro
s r r r rB q
D p j
D p j
aS (
= ∆ uv m ∆IS B
,
-p
t r r r rB
,
aS (
re
where
D p j
F = ∆ uv m ∆IS B
lP
o = BA
aS
D k j
G k j
,
D k j G k j
Fw
Fw
na
3.2. Entropy weighting method
ur
The entropy weighting method is a widely-accepted technique to decide the
Jo
diverse attributes weights in solving MADM problems without any additional or subjective information (He et al., 2016). Basic procedures of the entropy weighting method based on the evaluation information in I2LIFN form are presented as follows: 1) establish the evaluation matrix A=(aij)n×m (i=1, 2, …, n; j=1, 2, …, m), where aij represents evaluation information of the i-th alternative under the j-th attribute; 2) calculate entropy values of attributes through Eq. (2) and 3) determine the weights of attributes by:
ωC = j
1 − EC j
∑ (1 − E ) m
d =1
(4)
Cd
3.3. RT The RT which initially originated from economics and psychology was first put forward by Bell (1982) and has been utilized in the decision making field. Its basic 13
idea is that the decision makers not only focus on the results of the scheme that they finally choose, but also pay attention to the comparison results between the scheme and others that they do not choose. Generally speaking, RT can be employed to quantitate the degree of regret and rejoice of the decision makers for each alternative scheme by pair comparisons. Three core functions, i.e., utility function v(x),
regret-rejoice function R(Δv) and comprehensive perception function .
, jointly
play an important role in the quantification process of RT. Therefore, main steps of RT can be divided into three parts. First of all, the evaluation information x will obtain its utility value through v(x). ,
D C
F,B
G C
,
values are obtained via:
G C
FH , AB
D C
,
D C
% =x
F,B
G C
with
,
G C
C
re
∆Dz U|}D ,~}D V C C
lP
∆Dz {|€G ,~€G •
where %
C
C
∆Dz U|€D ,~€D V
ur
na
% =x
C
v ( x) =
I2LIFN
FHF , its corresponding utility
∆Dz {|}G ,~}G • C
an
of
D C
information
ro
W = BAB
evaluation
-p
For
C
'
d
(5)
'
d
(6)
1 − e− β x
(7)
β
refers to the membership degree utility value and the bigger the better,
Jo
while %
is the non-membership degree utility value and the smaller the better.
is the utility function (Bell 1982; Peng et al., 2019), β is the risk aversion coefficient
with 0 < β < 1. The greater β is, the greater degree of risk aversion the decision maker will face. Note that the utility value varies greatly with respective to different
β values, as shown in Fig. 1. The value of β will affect the final results, and we will choose the commonly used β value in the literature as the final value of β. f(x)is the distribution
AB
D C
,
D C
F,B
function G C
,
G C
related
to
AB
D C
,
D C
F,B
G C
,
G C
FH
and
FH. Generally, when evaluation information is given in the
interval form, normal distribution is commonly considered. For an interval evaluation information •
z
,
z
,
i
,
i
‚, its normal distribution function '(
is defined 14
as follow:
=
∆Dz |‡z ,~‡z J∆Dz |‡i ,~‡i X
=
√X „
, ˆ=
e
∆Dz
UI
jD} i V i†i
‰2 , ‰2
I∆Dz Š
(8) ‰1 , ‰1
.
-p
ro
of
where
'(
S
Fig. 1. The utility function v(x)
re
And then, regret values and rejoice values will be obtained through R(Δv). For a
D k! Œ
,
D k! Œ
V,U
G k! Œ
,
G k! Œ
V• , ‹U
D k! Œ
,
na
U‹U
lP
group of evaluation information on attribute Cj of alternative Ai denoted as ̃ # = D k! Œ
V,U
G k! Œ
,
G k! Œ
V•V, its corresponding regret
Jo
ur
value and rejoice value are obtained by the following: +
ℎ
+* # = Ž
ℎ* # = Ž
+ ℎ
where +
#
and ℎ
#
# #
=• =•
#
#
=+ =ℎ 0,
#
#
%#−%
%#−% 0,
0,
%
#
++ +ℎ
#
#
%# ≥% #
#
(9) (10) #
,% # < %
,% # ≥ %
%# <% %# <%
# #
− % # ,% # ≥ %
% # − % # ,% # < % 0, %# ≥% #
R ( ∆v) = 1− exp ( −γ ×∆v)
#
#
#
#
(11)
(12)
(13)
(14) (15)
represent the regret value and rejoice value of alternative A
with respect to that of alternative A
under attribute C# , respectively. ℎ* # and +* #
represent the rejoice value and regret value of membership degree of alternative A
15
with respect to that of alternative A
under attribute C# , respectively; ℎ
and +
#
are positive numbers and the bigger the better, while +* # and +
#
#
represent the rejoice value and regret value of non-membership degree of alternative
A with respect to that of alternative A ℎ* # and ℎ
#
under attribute C# , respectively. Generally, ∆
are negative numbers and the bigger the better.
is the regret-rejoice function
and parameter Δv represents the difference between two utility values and γ∈(0, +∞) is the regret aversion coefficient (Bell 1982; Chorus et al., 2012). Note that the regret-rejoice value also ranges widely with respective to different γ values, as shown
ur
na
lP
R( v)
re
-p
ro
used γ value in the literature as the final value of γ.
of
in Fig. 2. The value of γ will also affect the final results, and we choose the commonly
∆
Jo
Finally, the comprehensive perception function . Fig. 2. The regret-rejoice function
is used to find
comprehensive perception value of each alternative scheme through ( 4 = ∑‘ #aS m ! ∑ aS +
.
- A
=’
( = ∑‘ #aS m ! ∑ aS ℎ
“ E I“ G “ G I“ D
+ 1−’
#
#
” E I” D ” G I” D
(16) (17) (18)
where R(Ai) and H(Ai) represent the regret value and the rejoice value of alternative
Ai. m
!
that represents the weight of attribute C# is determined by the entropy
weighting method.
J
= max
A ,
I
= min
A , - J = max - A
and
- I = min - A . ’ is the balance factor and ranges from zero to one, and to avoid
the loss of generality, the value of ’ is set as 0.5 in this paper.
3.4. Integrated assessment process for scheme selection of DFD 16
The main steps of our proposed I2LI-RT method for scheme selection of DFD based on sustainability are presented as follows. Note that the general structure of I2LI-RT method is illustrated in Fig. 3 and environmental indicators and disassembly indicators are considered in assessment attributes. First of all, we give the following settings: there exist n alternatives marked in {A1, …, Ai, …, An} that have m attributes marked in {C1, …, Cj, …, Cm} for the decision maker to determine; a group of e experts marked in {E1, …, Ek, …, Ee} give their evaluation information
#
š
on the
i-th alternative under the j-th attribute; the weights vector to experts is , = satisfying
∑ek=1 λk = 1 and 0 ≤ › ≤ 1.
of
n
Jo
ur
na
lP
re
-p
ro
›S , ›X , … , ›•
Fig. 3. The framework of the proposed hybrid MADM method I2LI-RT
Step 1. Decide an LTS ST for scheme selection of DFD, and then obtain the initial
evaluation matrices ž Ÿ = B š
U‹
D !
š
,
G !
š
from set ST.
•,‹
D !
š
,
G !
š
#
š
F
(ב
.
#
š
•V and the elements in
is given in the form of #
š
#
š
=
are linguistic terms selected
17
Step 2. Transform ž Ÿ
š
into standardization matrices ž Ÿ = B
following standardization strategy: #
=¡
U‹
D !
,
G !
B
•=‹
#
š
D !
F
š
,
G !
š
•,‹
D !
,
G !
•=‹
¢ ∈ £J D !
š
,
G !
#
š
F
(ב
through the
19
•V ¢ ∈ £I
where £J indicates the index set where corresponding attributes are benefit
attributes; £I indicates the index set where corresponding attributes are cost attributes.
Step 3. Convert the evaluation information in ž Ÿ into 2-tuples by function ∆ ∙ defined in Herrera et al. (2000). Then obtain I2LIFN matrices ž Ÿ = B ̃ # F ̃#
(ב
.
based on ž Ÿ and the
of
Step 4. Establish the comprehensive matrix ž =
(ב
ro
weights vector , assigned to the experts, where ̃ # is obtained by Eq. (3). the weights m
!
-p
Step 5. Entropy values of various attributes are obtained via Eq. (2) and then obtain via Eq. (4).
based on ž. Elements in T are in
re
Step 6. Establish the utility matrix ¦ = % #
(ב
lP
the form of % # = % *# , % # , where % *# and % # are calculated by Eqs. (5)–(8).
na
Step 7.1. Calculate the membership degree regret matrices §¨ = + membership degree rejoice matrices ª¨ = ℎ
ur
and (12);
©
©
# (×(
# (×( and
under attribute Cj via Eqs. (11)
Jo
Step 7.2. Calculate the non-membership degree regret matrices §«¨ = + the non-membership degree rejoice matrices ª«¨ = ℎ Eqs. (13) and (14);
Step 7.3. Establish the regret matrices §¨ = + ª¨ = ℎ
# (×(
the
# (×(
# (×(
# (×( and
under attribute Cj via
and the rejoice matrices
under attribute Cj by Eqs. (9) and (10);
Step 8. Calculate the regret value
A
alternative Ai by adopting Eq. (16) and (17);
and the rejoice value - A
of each
Step 9. For each alternative A , find its associated comprehensive perception value . A
by Eq. (18).
Step 10. Order the alternatives according to . A
and select the optimal alternative
that has the highest value.
18
4. Experimental results and discussions 4.1. Case study Sustainable production and assessment have been essential for manufacturers and policy makers. In the summit of G20, sustainability is even regarded as one of the most crucial issues. Refrigerators are one of the common household appliances in China. According to the media reported, the number of waste refrigerators in different provinces and cities was increasing in the past decades, which brought great burdens to the environment protection and exacerbated the greenhouse effect. Exactly, China
of
increased its refrigerator capacity with an annual growth rate of 8.2% and generated
ro
89.92 million refrigerators in 2015 (Xiao et al., 2016). Also, highly valued materials or components in waste refrigerators have stimulated the unregulated recycling
-p
activities, which leads to severe pollution on the local soil and groundwater (Tian et
re
al., 2018b).
Great efforts have been made in addressing this tricky problem. In recent years,
lP
China has drawn up a series of policies and regulations to require manufacturers to
na
recycle obsolete refrigerators to reduce their life-cycle environmental impacts. Besides, some advanced and sophisticated disassembly technologies used for
ur
recovering the materials from obsolete refrigerators are published in articles and some of those technologies are introduced in real applications. Nevertheless, deciding how
Jo
to evaluate the refrigerators schemes of DFD based on sustainability remains to be resolved. Therefore, we evaluate four kinds of refrigerator alternatives via the proposed I2LI-RT method and a designed eight-criterion scheme evaluation system. In the case study, four refrigerator design schemes (namely A1-A4) are obtained from Tian et al. (2018b), Liu (2004) and Guo et al. (2015), and detailed parameters of the four refrigerator design schemes are shown in Table 1. To establish a comprehensive evaluation system to assess each alternative for sustainability objectively, original data are collected from Guo et al. (2015) and Tian et al. (2018b) and questionnaires done by experts with professional knowledge and rich working experience in the DFD field, e.g., scholars of university and supervisors of enterprise (Safaeian et al., 2019). Finally, a comprehensive evaluation system with eight core criteria including disassembly and environmental characteristics, i.e., disassembly energy consumption (kW·h) (C1), disassembly accessibility (C2), fastener ratio (C3), 19
toxic material proportion (C4), material recovery rate (C5), disassembly expense (Yuan) (C6), production and use noise (dB) (C7), and waste emissions (mg) (C8) is established. The illustration of those criteria is presented in Fig. 4, where cost criteria are marked in brown and benefit criteria are marked in green, and discussion of those criteria is present in Section 4.5. The evaluation LTS is chosen as: S7= {s0 =Extremely Terrible, s1 =Terrible, s2 =Medium Terrible, s3 = Ordinary, s4 = Medium Fine, s5 = Fine, s6 = Extremely Fine}. Three additional experts (namely E1, E2 and E3) are invited to give their evaluation information based on the seven-level LTS and their evaluation results on the four alternatives are shown in Tables 2-4. In general, the weights vector S S S n
assigned to experts is set to , = B , , F .
Jo
ur
na
lP
re
-p
ro
of
g g g
Fig. 4. Comprehensive evaluation system of scheme of DFD based on sustainability
Table 1. Detailed parameters of the four refrigerator design schemes C1(kW·h)
C2
C3(%)
C4(%)
C5(%)
C6(/Yuan)
C7(dB)
C8(mg)
A1
0.53
0.8
0.5
1.4
40
45
110
16.1040
A2
0.62
0.7
0.6
1.4
40
50
108
16.1040
A3
0.68
0.6
0.7
1.5
42
55
112
13.0115
A4
0.52
0.5
0.3
0.1
35
51
105
13.9416 20
š
A1 A2 A3 A4
A4
([s2, s2],
([s1, s2],
([s1, s2],
[s0, s0])
[s3, s4])
[s4, s4])
([s5, s5],
([s0, s0],
([s0, s1],
[s2, s4])
[s0, s1])
[s4, s6])
[s3, s5])
([s1, s3],
([s4, s5],
([s1, s1],
[s2, s3])
[s0, s0])
([s0, s0], [s6, s6])
C6
([s4, s4],
C7
C8
([s1, s1],
([s0, s1],
([s1, s2],
[s1, s2])
[s3, s5])
[s2, s4])
[s4, s4])
([s3, s5],
([s0, s2],
([s0, s1],
([s1, s1],
[s1, s1])
[s4, s4])
[s2, s5])
[s3, s5])
([s0, s2],
([s5, s6],
([s2, s2],
([s0, s3],
([s0, s0],
[s3, s5])
[s2, s4])
[s0, s0])
[s2, s4])
[s1, s3])
[s3, s6])
([s3, s4],
([s0, s0],
([s0, s0],
([s3, s4],
([s1, s2],
([s0, s0],
([s0, s1],
[s0, s2])
[s4, s5])
[s5, s6])
[s1, s2])
[s3, s4])
[s4, s6])
[s4, s5])
C2
C3
C4
C5
([s1, s1],
([s6, s6],
([s0, s0],
([s1, s1],
([s4, s4],
of
C1
C6
C7
C8
([s0, s1],
([s0, s0],
[s4, s5])
[s0, s0])
[s5, s6])
[s4, s5])
[s1, s1])
[s4, s5])
[s5, s5])
[s5, s6])
([s3, s5],
([s0, s1],
([s2, s2],
([s2, s4],
([s0, s2],
([s1, s2],
([s0, s1],
[s4, s4])
[s1, s1])
[s3, s5])
[s3, s4])
[s0, s2])
[s3, s4])
[s4, s4])
[s4, s5])
([s0, s1],
([s4, s4],
([s1, s1],
([s2, s2],
([s3, s4],
([s1, s1],
([s0, s2],
([s0, s1],
[s4, s5])
[s0, s1])
[s4, s5])
[s4, s4])
[s0, s1])
[s4, s4])
[s2, s4])
[s4, s4])
([s1, s2],
([s3, s4],
([s1, s1],
([s0, s2],
([s4, s5],
([s1, s1],
([s1, s1],
([s0, s1],
[s3, s4])
[s0, s2])
[s4, s4])
[s4, s4])
[s1, s1])
[s4, s5])
[s4, s4])
[s3, s5])
re
-p
([s1, s1],
([s1, s2],
ro
A4
A3
[s3, s5])
C5
lP
A3
A2
([s5, s6],
C4
na
š
A2
A1
([s0, s1],
C3
Table 3. The original evaluation information given by expert E2
A1
ž®
C2
Table 4. The original evaluation information given by expert E3 š
C1 ([s0, s0],
C2
C3
C4
C5
C6
C7
C8
([s4, s6],
([s2, s2],
([s1, s2],
([s5, s5],
([s1, s1],
([s1, s1],
([s0, s1],
ur
ž-
C1
Jo
ž¬
Table 2. The original evaluation information given by expert E1
([s1, s1],
[s4, s5])
[s0, s1])
[s4, s5])
[s4, s5])
[s1, s2])
[s4, s4])
[s4, s4])
[s4, s5])
([s0, s1],
([s3, s5],
([s1, s1],
([s1, s2],
([s4, s4],
([s0, s1],
([s2, s2],
([s2, s3],
[s3, s4])
[s0, s0])
[s3, s4])
[s3, s4])
[s1, s1])
[s4, s4])
[s3, s3])
[s3, s3])
([s0, s1],
([s4, s4],
([s0, s0],
([s2, s2],
([s3, s4],
([s1, s2],
([s1, s2],
([s1, s2],
[s3, s5])
[s0, s2])
[s3, s5])
[s3, s3])
[s1, s2])
[s3, s4])
[s3, s3])
[s4, s4])
[s5, s6])
[s0, s0])
[s4, s4])
[s4, s4])
[s0, s1])
[s4, s5])
[s3, s5])
[s4, s4])
([s1, s1],
([s5, s5],
([s0, s1],
([s4, s4],
([s1, s1],
([s1, s1],
([s1, s1],
4.2. Results obtained by proposed I2LI-RT After reviewing the existing studies on RT,
is set to 0.02 and
is set to 0.3.
According to the main steps on the I2LI-RT method mentioned in Section 4.2, we get the calculation results step by step. Step 2. Standardization matrix ž ¬ is shown in Table 5 as an example.
21
Table 5. The standardization matrix ž ¬
ž¬
C1
A1 A2 A3 A4
C2
C3
C4
C5
C6
C7
C8
([s3, s5],
([s5, s6],
([s3, s4],
([s4, s4],
([s4, s4],
([s3, s5],
([s2, s4],
([s4, s4],
[s0, s1])
[s0, s0])
[s2, s2])
[s1, s2])
[s1, s2])
[s1, s1])
[s0, s1])
[s1, s2])
([s2, s4],
([s5, s5],
([s4, s6],
([s3, s5],
([s3, s5],
([s4, s4],
([s2, s5],
([s3, s5],
[s1, s2])
[s0, s1])
[s0, s0])
[s0, s1])
[s1, s1])
[s0, s2])
[s0, s1])
[s1, s1])
([s2, s3],
([s4, s5],
([s3, s5],
([s2, s4],
([s5, s6],
([s2, s4],
([s1, s3],
([s3, s6],
[s1, s3])
[s0, s0])
[s1, s1])
[s0, s2])
[s0, s0])
[s2, s2])
[s0, s3])
[s0, s0])
([s6, s6],
([s3, s4],
([s4, s5],
([s5, s6],
([s3, s4],
([s3, s4],
([s4, s6],
([s4, s5],
[s0, s0])
[s0, s2])
[s0, s0])
[s0, s0])
[s1, s2])
[s1, s2])
[s0, s0])
[s0, s1])
A3 A4
C4
C5
C6
C7
C8
([(s3, 0), (s5, 0)],
([(s5, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s4, 0)],
[(s0, 0), (s1, 0)])
[(s0, 0), (s0, 0)])
[(s2, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
([(s4, 0), (s4, 0)], [(s1, 0), (s2, 0)])
([(s3, 0), (s5, 0)], [(s1, 0), (s1, 0)])
([(s2, 0), (s4, 0)],
([(s4, 0), (s4, 0)],
[(s0, 0), (s1, 0)])
[(s1, 0), (s2, 0)])
([(s2, 0), (s4, 0)],
([(s5, 0), (s5, 0)],
([(s4, 0), (s6, 0)],
([(s3, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
([(s4, 0), (s4, 0)],
([(s2, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
[(s1, 0), (s2, 0)])
[(s0, 0), (s1, 0)])
[(s0, 0), (s0, 0)])
[(s0, 0), (s1,0)])
[(s1, 0), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 0), (s1, 0)])
[(s1, 0), (s1, 0)])
([(s2, 0), (s3, 0)],
([(s4, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
([(s2, 0), (s4, 0)],
([(s5, 0), (s6, 0)],
([(s2, 0), (s4, 0)],
([(s1, 0), (s3, 0)],
([(s3, 0), (s6, 0)],
[(s1, 0), (s3, 0)])
[(s0, 0), (s0, 0)])
[(s1, 0), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 0), (s0, 0)])
[(s2, 0), (s2, 0)])
[(s0, 0), (s3, 0)])
[(s0, 0), (s0, 0)])
([(s6, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s5, 0)],
([(s5, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s6, 0)],
([(s4, 0), (s5, 0)],
[(s0, 0), (s0, 0)])
[(s0, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
[(s0, 0), (s0, 0)])
[(s0, 0), (s1, 0)])
-p
C3
re
A2
C2
lP
A1
C1
na
ž¬
ro
Table 6. I2LIFN matrix ž ¬
of
Step 3. I2LIFN matrix ž ¬ is shown in Table 6 as an example.
[(s0, 0), (s0, 0)])
[(s0,0), (s0, 0)])
ur
Step 4. The comprehensive matrix ž is shown in Table 7.
Jo
Step 5. The entropy values of eight attributes are presented in Table 8 and their corresponding normalized weights are presented in Table 9. Based on the results, we get that disassembly accessibility (C2), fastener ratio (C3), disassembly waste emissions (C8), and disassembly energy consumption (C1) have a large impact on scheme selection of DFD based on sustainability since those attributes carry the relatively larger weights. Table 8. The entropy values of eight attributes E(C# )
C1
C2
C3
C4
C5
C6
C7
C8
0.3711
0.2847
0.3480
0.4105
0.3881
0.4066
0.4360
0.3611
Table 9. The weights of eight attributes obtained by entropy weighting method m
!
C1
C2
C3
C4
C5
C6
C7
C8
0.1259
0.1432
0.1306
0.1180
0.1225
0.1188
0.1129
0.1279
22
Step 6. The utility matrix ¦ = % #
(ב
is shown in Table 10.
Table 10. The utility matrix
¦
C1
C2
C3
C4
C5
C6
C7
C8
A1
(4.4430, 0.4961)
(5.1940, 0)
(4.1395, 1.3157)
(3.9870, 1.3120)
(4.1509, 0.9873)
(4.1392, 0.8242)
(3.8334, 0.8242)
(4.2918, 0.6603)
A2
(3.6799, 1.3120)
(4.4434, 0.6603)
(4.2911, 0.4961)
(3.8334, 0.9873)
(3.5255, 1.1498)
(3.6801, 0.9869)
(3.6799, 0.9873)
(4.1392, 0.8242)
A3
(3.5709, 0.9869)
(3.9867, 0.1659)
(3.8334, 0.9901)
(3.3709, 1.4735)
(4.1395, 0.4961)
(3.5258, 1.1500)
(2.5893, 1.4730)
(3.6799, 0.9873)
A4
(4.2916, 0.6603)
(3.5258, 0.9863)
(3.9867, 0.3322)
(3.9870, 0.9873)
(3.6799, 1.3120)
(3.6799, 1.3120)
(3.8337, 0.8242)
(3.9867, 0.8239)
Step 7.1. The membership degree regret matrix §¬ and the membership degree ©
rejoice matrix ª¬ under attribute CS are shown in Table 11 as an example. ©
Table 11. The membership degree regret matrix §¬ and the membership degree rejoice matrix ª¬ under attribute C1 Regret matrix §¬ A2
A3
A4
A1
©
©
A2
A3
A4
0
0.2046
0.2750
0.0444
0
0
0.0885
0
-p
A1
Rejoice matrix ª¬
ro
©
C1
of
©
0
0
0
0
A2
-0.2573
0
0
-0.2014
A3
-0.3794
-0.0971
0
-0.3181
0
0
0
0
A4
-0.0465
0
0
0
0
0.1677
0.2413
0
lP
re
A1
Step 7.2. The non-membership degree regret matrix §«¬ and the non-membership
na
degree rejoice matrix ª«¬ under attribute CS are shown in Table 12 as an example.
ur
Table 12. The non-membership degree regret matrix §«¬ and the non-membership degree rejoice matrix ª«¬ under attribute C1 Regret matrix §«¬
Jo
C1
A1
A2
A3
A4
A1
0
0
0
0
A2
-0.2773
0
-0.1025
A3
-0.1586
0
A4
-0.0505
0
A1
Rejoice matrix ª«¬ A2
A3
A4
0
0.2171
0.1369
0.0481
-0.2159
0
0
0
0
0
-0.1029
0
0.0929
0
0
0
0
0
0.1776
0.0933
0
Step 7.3. Regret matrix §¬ and rejoice matrix ª¬ under attribute CS are shown in Table 13 as an example.
Table 13. Regret matrix §¬ and rejoice matrix ª¬ under attribute C1
C1 A1
Regret matrix §¬ A2
A3
A4
A1
Rejoice matrix ª¬ A2
A3
A4
A1
0
0
0
0
0
0.4218
0.4119
0.0925
A2
-0.5346
0
-0.1025
-0.4174
0
0
0.0885
0
A3
-0.5380
-0.0971
0
-0.4210
0
0.0929
0
0
A4
-0.0970
0
0
0
0
0.3452
0.3347
0 23
ro o
f
Table 7
re -p
The comprehensive matrix
C2
C3
C4
C5
C6
C7
C8
([(s4, 0), (s5, 1/3)],
([(s5, 0), (s6, 0)],
([(s4, 0), (s5, -1/3)],
([(s4, 0), (s4, 1/3)],
([(s4, 1/3), (s4, 1/3)],
([(s4, -1/3), (s5, 0)],
([(s3, 1/3), (s5, -1/3)],
([(s4, 1/3), (s5, -1/3)],
[(s0, 1/3), (s1, -1/3)])
[(s0, 0), (s0, 0)])
[(s1, 1/3), (s1, 1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s1, 0)])
[(s1, -1/3), (s1, 0)])
[(s0, 1/3), (s1, 0)])
([(s3, 1/3), (s4, 1/3)],
([(s4, 1/3), (s5, 0)],
([(s4, -1/3), (s5, 1/3)],
([(s3, 1/3), (s5, -1/3)],
([(s3, 0), (s4, 1/3)],
([(s4, -1/3), (s4, 0)],
([(s3, 1/3), (s4, 1/3)],
([(s4, -1/3), (s5, 0)],
[(s1, 0), (s2, -1/3)])
[(s0, 1/3), (s1, 0)])
[(s0, 1/3), (s1, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s2, -1/3)])
[(s0, 1/3), (s2, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s1, 0)])
([(s3, 0), (s4, 0)],
([(s4, -1/3), (s5, -1/3)],
([(s3, 1/3), (s5, -1/3)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s5, -1/3)],
([(s3, 1/3), (s4, 0)],
([(s2, 0), (s3, 1/3)],
([(s3, 1/3), (s4, 1/3)],
[(s0, 1/3), (s2, -1/3)])
[(s0, 0), (s0, 1/3)])
[(s1, 0), (s1, 0)])
[(s1, 0), (s2, 0)])
[(s0, 1/3), (s1, -1/3)])
[(s1, 0), (s1, 1/3)])
[(s1, -1/3), (s2, 1/3)])
[(s1, -1/3), (s1, 1/3)])
([(s4, 0), (s5, 0)],
([(s3, 1/3), (s4, 0)],
([(s3, -1/3), (s5, -1/3)],
([(s4, 0), (s4, 1/3)],
([(s3, 1/3), (s4, 1/3)],
([(s3, 1/3), (s4, 1/3)],
([(s4, -1/3), (s4, 1/3)],
([(s4, -1/3), (s5, -1/3)],
[(s0, 1/3), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 1/3), (s0, 1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, -1/3), (s1, 0)])
[(s0, 1/3), (s1, 1/3)])
Jo
ur
na
lP
C1
24
Step 8. Regret values presented as follows:
A4
A3
A2
A1
A
and rejoice values - A
of each alternative A are
AS = −0.1443, - AS = 0.6293;
AX = −0.3874, - AX = 0.3030; Ag = −0.7686, - Ag = 0.2006; A^ = −0.4629, - A^ = 0.3007.
Step 9. The comprehensive perception values . A
for each alternative A are
shown as follows:
of
. AS = 0.5000, . AX = −0.0753, . Ag = −0.5000, . A^ = −0.1385.
Step 10. Therefore, we find the final rank: AS > AX > A^ > Ag . That is, AS is the
ro
optimal design scheme according to the I2LI-RT method, followed by AX , A^ and
re
-p
Ag .
lP
4.3. Comparative studies with other state of art methods
na
a. Comparison with the information entropy measure In this subsection, we extend the information entropy measure to I2LIFNs, and
ur
the case study will be solved again by the new method called I2LI-IEM for short.
Jo
According to Zhao et al. (2016), alternatives are ranked by comparing the amount of determinate information. We calculate the amount of determinate information of each alternative and
obtain: /0 AS = 0.6894 ,
/0 AX = 0.6027 ,
/0 Ag = 0.5714 ,
0.5833. Therefore, we have the following rank: AS > AX > A^ > Ag .
/ 0 A^ =
b. Comparison with the GC method In this subsection, we develop the GC method to I2LIFNs. The case study will be solved again by the new fuzzy GC method called I2LI-GC for short. Some adaptive approaches based on I2LI-GC and our experimental conditions are adopted.
We calculate the GC closeness index 1 for each alternative and get: 1S =
0.3935,
1X = 0.4993,
1g = 0.5952,
rank: AS > AX > A^ > Ag .
1^ = 0.5008. So, we have the following
c. Comparison with the TOPSIS method 25
Hu et al. (2007) proposed the TOPSIS method for solving an MADM problem with fuzzy evaluation information. In this subsection, we extend this method to I2LIFNs, and the case study will be solved again by the new fuzzy TOPSIS method called I2LI-TOPSIS for short.
We work out the distance closeness index 23 for each alternative and obtain:
23z = 0.2649 , 23i = 0.2701 , 23³ = 0.5278 , 23´ = 0.4641 . So, we have the following rank: AS > AX > A^ > Ag
d. Comparison with IVLIFNs and RT
of
I2LIFNs can be regarded as a variant of IVLIFNs (Liu et al., 2017), so in this comparison experiment, we decide to adopt the IVLIFNs to represent and process the
ro
evaluation information. Furthermore, to confirm the effectiveness of the I2LI-RT
-p
method, RT is also used to decide the final order and the best alternative. Note that we call this integrated method IVLI-RT for short.
and get: . 0 AS =
re
We compute the comprehensive perception values . 0 A
0.5000, . 0 AX = −0.2931, . 0 Ag = −0.4773, . 0 A^ = −0.0692. So, we have
na
lP
the following rank: AS > A^ > AX > Ag
e. Discussions between I2LI-RT and the comparative studies
ur
For ease of analysis, we put all the ranking results together obtained by the five
Jo
methods, i.e., I2LI-RT, I2LI-IEM, I2LI-GC, I2LI-TOPSIS and IVLI-RT, in Table 14. It can be seen that A1 is the optimal scheme based on the I2LI-RT method or the rest four comparison methods. Thus, the effectiveness of the I2LI-RT method is verified. The ranking results of I2LI-RT, I2LI-IEM, I2LI-GC and I2LI-TOPSIS methods are mainly accordant, which demonstrates the combination of I2LIFNs and the RT is rational and practicable to conduct scheme selection of DFD based on sustainability.
Table 14. Ranking results obtained by I2LI-RT method and four comparison methods I2LI-RT
. A
I2LI-IEM
Rank
A1
0.5000
1
A2
-0.0753
A3 A4
/0 A
I2LI-GC
Rank
I2LI-TOPSIS
1
Rank
23
Rank
0.6894
1
0.3935
1
0.2649
1
2
0.6027
2
0.4993
2
0.2701
-0.5000
4
0.5714
4
0.5952
4
-0.1385
3
0.5833
3
0.5008
3
IVLI-RT
.0 A
Rank
0.5000
1
2
-0.2931
3
0.5278
4
-0.4743
4
0.4641
3
-0.0692
2
26
However, some differences exist among those ranking results. For the I2LI-IEM method, although the ranking result is the same as that obtained by I2LI-RT, I2LI-IEM cannot tell how well or bad an alternative scheme is. In our proposed I2LI-RT, the worse the scheme is, the greater the probability that its corresponding value becomes a small negative number. Moreover, a set of reasonable parameters in I2LI-RT can help enlarge the difference gap between schemes. For the I2LI-GC method, it does not determine the better one between the schemes A2 and A4 due to that their corresponding gray closeness indices are relatively close, while our I2LI-RT method can do it. This is due to the fact that the GC method cannot report the distance among information sequences and the RT essentially has the property of
of
distance comparison. For the I2LI-TOPSIS method, it can be seen that 23z is
ro
approximately the same as 23i . In fact, A1 is not slightly better than A2, thus using
-p
I2LI-TOPSIS may not clearly reflect actual conditions; while the proposed I2LI-RT
re
method can have a relatively strong ability to resolution. This is because that
information sequences.
lP
regarding distance as the unique measure will not tell the situation changes among
na
As Table 14 demonstrates, A2 ranks before A4 and A3 ranks after A4 using the IVLI-RT method, while A2 ranks after A4 and A3 ranks before A4 using the rest four
ur
methods. The explanation for the ranking inconsistences mainly depends on the features of the comparison methods. The IVLI-RT method adopts IVLIFNs to
Jo
evaluate the performance of the four alternative schemes. However, the proposed I2LI-RT method uses I2LIFNs for assessing those schemes, which can not only capture the vagueness and uncertainty of evaluation information given by experts, but also reduce information loss/distortion in the aggregation phase. 4.4.Sensitivity analysis The sensitivity analysis is also conducted to measure the robustness of I2LI-RT method by adjusting the attributes weights (Feng et al., 2019b). Considering the amount of attributes used in the case study, thirteen experiments are designed to record the final rank and the experimental outcome is shown in Table 15.
Table 15. Experimental outcome of sensitivity analysis for thirteen experiments Expt
Weights
Comprehensive perception values . A
Rank 27
2 3 4 5 6 7 8 9 10 11 12
m ³ =0.825, m m ´ =0.825, m m ¶ =0.825, m m · =0.825, m
m m m m
z, ³I
zI ¶ zI ³ zI zI
-0.4463
-0.5000
A^
0.2580
1>4>2>3
0.5000
-0.0232
-0.0512
-0.5000
1>2>3>4
=0.025
-0.3280
0.5000
-0.5000
0.3483
2>4>1>3
=0.025
0.3237
0.3680
-0.5000
0.5000
4>2>1>3
=0.025 µ
=0.025 µ
zI ³, ¶I µ zI ´, ·I
0.3166
-0.4846
0.4963
-0.5000
3>1>2>4
=0.025 µ
0.5000
-0.1026
-0.5000
-0.4178
1>2>4>3
=0.025
0.5000
0.2588
-0.5000
0.4263
1>4>2>3
0.5000
0.1113
-0.5000
-0.0260
1>2>4>3
0.5000
-0.0610
-0.5000
-0.0922
1>2>4>3
=0.075
0.5000
-0.1411
-0.5000
-0.1686
1>2>4>3
=0.155
0.5000
-0.0439
-0.5000
-0.0631
1>2>4>3
=0.050 µ
0.5000
-0.0062
-0.5000
-0.0314
1>2>4>3
0.5000
-0.1309
-0.5000
-0.1729
1>2>4>3
zI ¶, ¸I
zI ·, µ
m µ =0.825, m zI
0.5000
Ag
zI i, ´I µ
m ¸ =0.825, m m
iI
AX
zI
=0.025 ¸
=0.125 µ
=0.155, m =0.075, m
=0.200, m ´ =0.050, m ´
·I µ ´I µ ¶I ¶I
=0.200 µ
-p
13
m i =0.825, m
AS
=0.025 µ
of
1
m z =0.825, m
ro
No.
From Table 15, it can be observed that the weight of each attribute is set to be bigger one by one in the first eight experiments. Weights of these eight attributes are
lP
re
set to be equal in the ninth experiment, which is m
zI µ
=0.125. In the tenth
experiment, attributes C1–C5 share a weight of 0.775 equally and attributes C6–C8
na
share a weight of 0.225 equally. Contrary to the tenth experiment, the first three attributes share a weight of 0.225 equally and the last five attributes share a weight of
ur
0.775 equally in the eleventh experiment. In the twelfth experiment, attributes C1–C4
Jo
share a weight of 0.800 equally and the rest four attributes C5–C8 share a weight of 0.200 equally. Contrary to the twelfth experiment, the first four attributes share a weight of 0.200 equally, while the last four attributes share a weight of 0.800 equally in the thirteenth experiment. Meanwhile, Fig. 5 illustrates the outcome of sensitivity analysis. Note that the comprehensive perception value . A
can be found in Table
15.
28
Fig. 5. Results of sensitivity analysis for thirteen experiments
It can be found from Table 15 and Fig. 5 that, among 10 out of 13 experiments, scheme A1 has the highest comprehensive perception value. Thus, the proposed
I2LI-RT method is relatively robust to the criteria weights m
!
with A1. In other
words, the proposed scheme evaluation method of DFD is feasible and robust. Besides, the ultimate rank of those schemes would change greatly with respective to different criteria weights, which suggested the importance of selecting qualified experts for sustainable performance evaluation of schemes for DFD.
of
4.5.Discussions
ro
In this section, we discuss the experimental results from two aspects, i.e., 1) criteria analysis and improvement measures and 2) advantages of the proposed
-p
I2LI-RT method.
re
a. Criteria analysis and improvement measures
As can be seen in Section 4.2, the weights of these eight criteria are obtained by
lP
using the proposed I2LI-RT method and those weights are plotted in Fig. 6 where
Jo
ur
na
some implication can be derived.
Fig. 6. Plot of the calculated criterion weights
(1) Disassembly accessibility (C2), fastener ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on evaluation of DFD refrigerator schemes based on sustainability since these factors carry the larger weights and are also above the average weight 0.1250, while production and use noise (C7) has the smallest weight among the eight criteria; 29
(2) Disassembly accessibility (C2) that refers to how difficult it is for disassembly tools to approach the parts of refrigerators has a largest impact on evaluation of DFD schemes based on sustainability. Generally speaking, a good disassembly accessibility can lead to the reduction of number and category of disassembly tools and the improvement of processing efficiency, which is related to structural design and layout. A deeper position of parts to be disassembled will bring greater difficulty to disassembly operations, thus in refrigerator product design, the location of parts with high recycling values should be set where they are easily available. Besides, designers should leave a larger space for compressor
of
installation and simplify the installation method to facilitate installation and
ro
disassembly. Fastener ratio (C3) represents the proportion of the amount of connections in all elements and a smaller fastener ratio can make a better
-p
disassembly efficiency and promote the process of product recovery (Kondo et al.,
re
2003). Typical fasteners include bolts, studs, screws, nuts, washers, pins and so on. However, excessive utilization of fasteners will cause loose fit between
lP
components when the connection condition is not qualified. Waste emissions (C8) can be divided into waste solids, waste liquids and waste gases, which can pose
na
potential threats to human health and the global ecosystem (Lee et al., 2001; Tian
ur
et al., 2018a). Waste gases come from the organic waste gas emission during curing and waste liquids originate from the discharge of phosphating solution
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during phosphating treatment. Phosphate-rich solution is a nutrient-rich substance and discharging it without any chemical treatment will cause damage to the ecological environment, which does not satisfy the purpose of sustainable development. Disassembly energy consumption (C1) comes from various aspects and is mainly used to destroy the connection between components. Reasonable spatial layout and appropriate connection type can gain a lower disassembly energy consumption. For example, integrated connection type in which the coupling is integrated on the components can be adopted in refrigerator design. Production and use noise (C7) refers to the noise generated during the production and use of the refrigerator. Strong noise will cause hearing fatigue and even deafness for workers and users. Production noise comes from the installation of metal parts during the assembly process, as well as the process of punching and drilling during the assembly process. Use noise mainly comes from the start-up and operation of the compressor during use and the vibration of the pipeline in the 30
refrigerator during operation. And some improvement measures can be used to reduce those noise. For example, change the connection structure (reduce screws and riveting), reduce the portion of metal parts, use high-efficiency silent compressor, determine the optimal speed of the fan motor through the analysis of the pressure wave characteristics, optimize piping design and so on. As for toxic material proportion (C4), CFCs (chloro-fluoro-carbons) take a large part. Under normal conditions, CFCs are chemically stable and will evaporate at pretty low temperatures, thus they are ideal refrigerants for refrigerators and freezers. But CFCs will consume plenty of ozone in the ozone layer, which will destroy the
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ecological environment. At present, researches on CFCs alternative technology
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have made great progress and fluorine-free refrigerators have become mainstream products. The refrigerant has replaced R12 with R134a, and the blowing agent
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R11 has been replaced by cyclopentane (Liu 2004). Disassembly expense (C6)
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contains many aspects, such as labor costs, electricity costs and so on. Complex product designs will increase the expense of disassembly which will also lead to
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higher recovery costs. Reasonable structural design and appropriate material selection can reduce both energy disassembly consumption and disassembly
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expense. Material recovery rate (C5) depends on the structure of the refrigerator,
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the type of materials and compatibility among materials. Therefore, designers need to make a reasonable combination of parts (reduce the number of parts and
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the types of materials), choose compressors with less or no copper as much as possible, replace easy-to-soften PVC with other materials, and reduce the utilization of stainless steel products. b. Advantages
of the proposed I2LI-RT method
In the proposed I2LI-RT method, to better describe the fuzziness of human thinking, evaluate information is represented by I2LIFNs and the final optimal scheme is determined by RT. The adoption of I2LIFNs for representing and processing fuzzy information makes I2LI-RT easily capture the uncertainty of information and avoid information loss/distortion, and the introduction of RT assist I2LI-RT in objectively describing the emotions of decision makers by several pair comparisons, which are verified in Section 4.3. The sensitivity analysis in Section 4.4 demonstrates the robustness of the proposed method. In summary, the I2LI-RT method is effective and feasible to evaluate the sustainable performance of schemes of DFD. 31
5. Conclusion DFD is an effect product design technique from a disassembly point of review. A well-organized scheme of DFD should focus on both disassembly characteristics and environmental characteristics to achieve the goal of sustainable development. In this work, a hybrid MADM method, called I2LI-RT for short, was proposed to evaluate schemes of DFD based on sustainability under fuzzy environment. In the method, to better describe the fuzziness and ambiguity and avoid information loss/distortion in information aggregation phases, the concepts of I2LIFSs and I2LIFNs were firstly
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developed to represent the fuzzy evaluation information given by experts. In addition, an entropy weighting technology was utilized to determine the weights of different
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criteria and finally, RT was employed to order the alternatives and determine the
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optimal one.
As a case study has been applied, four refrigerator design schemes were selected
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as alternatives and an eight-criterion evaluation system of schemes of DFD for sustainability based on disassembly and environmental characteristics was established.
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Experimental results demonstrated that alternative AS was the optimal scheme based
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on fuzzy evaluation information, and disassembly accessibility (C2), fastener ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large
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impact on refrigerator’s sustainable design. Analysis of those criteria were conducted
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and the corresponding improvement measures of each criterion based on sustainability were also introduced. In addition, the comparative studies of I2LI-RT method with other four state of art methods indicated the feasibility and effectiveness of the proposed method and sensitivity analysis results verified its robustness and reliability. In summary, the proposed hybrid MADM method can be utilized to guide decision makers/manufacturers in making better decisions when choosing the most sustainable scheme of DFD. There are many future directions to provide new contributions for further research on the designation of a sustainable DFD scheme. First, encoding the hybrid MADM method and implanting the codes to computer programs for assessing schemes intelligently, can be suggested. Furthermore, employing the method to other application areas, such as environmental risk assessment, airlines safety evaluation and so on, is another challenging application for our paper. Due to the uncertainty and fuzziness of evaluation information, other uncertain theories can be integrated into the 32
proposed method (Zhang et al., 2020). At last but not least, integrating the proposed hybrid method with recent advances in the evolutionary computation is another interesting addition for future studies (Fathollahi-Fard et al., 2020).
Acknowledgement This work is supported in part by National Natural Science Foundation of China
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under Grant No. 51775238, Science and Technology Development Project of Jilin
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Province under Grant Nos 20180101060JC and 20180101058JC.
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Interest statement statement
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We claim no conflict of interest
S0959-6526(20)34768-5
DOI:
https://doi.org/10.1016/j.jclepro.2020.124724
Reference:
JCLP 124724
To appear in:
Journal of Cleaner Production
Received Date: 15 April 2020 Revised Date:
28 September 2020
Accepted Date: 16 October 2020
Please cite this article as: Wang W, Tian G, Zhang d T, Li F, Fathollahi-Fard AM, Wang D, Jabarullahg NH, Li Z, Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory, Journal of Cleaner Production, https://doi.org/10.1016/j.jclepro.2020.124724. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Elsevier Ltd. All rights reserved.
Credit author statement: Wenjie Wang: Wang Data curation, Writing-Original draft preparation. Guangdong Tian: Conceptualization, Methodology, Software. Tongzhu Zhang: Zhang Investigation and Data curation. Guangdong Tian, Tian, Fangyi Fangyi Li and Danqi Wang: Wang: Supervision.:: Amir Mohammad FathollahiFathollahi-Fard: Fard Software, Validation.: Noor H. Jabarrullah and Zhiwu Li: Writing-
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Reviewing and Editing.
Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory Wenjie Wang a,b, Guangdong Tian a,b,c,*, Tongzhu Zhang d, Fangyi Li a,b, Amir Mohammad Fathollahi-Fard e, Danqi Wang f,*, Noor H. Jabarrullahg, Zhiwu Li h,i
a. Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan, 250061, China b. National Demonstration Center for Experimental Mechanical Engineering Education, Shandong
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University, Jinan 250061, China
China
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c. School of Computer and Communication Engineering, Liaoning Shihua University, Fushun 113001,
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d. Automotive Standardization Research Institute, China Automotive Technology and Research Center, Tianjin 300300, China
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e. Department of Electrical Engineering, École de Technologie Supérieure, 1100 Notre-Dame St. W.,
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Montréal, Canada
f. State Key Laboratory of Automobile Simulation and Control, Jilin University, Changchun 130025,
na
China
g. Institute of Aviation Technology, University Kuala Lumpur, Selangor, Malaysia
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h. Institute of Systems Engineering, Macau University of Science and Technology, Taipa 999078, Macau, China
Jo
i. School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China Corresponding authors: G. D. Tian ([email protected]), D. Q. Wang ([email protected])
Abstract: Design for disassembly (DFD) is an essential design technique to consider the disassembly and recyclability of a product at the initial design stage. An efficient DFD technique provides the disassembling and recycling easily. However, the recent trends of disassembling and recycling are to consider the aspects of environmental and social sustainability. Due to shortage of energy and deterioration of the ecological environment, the sustainable production is an active research topic to use the economic and social benefits as the evaluation standard of a design scheme as well as its environmental characteristics. This paper provides a new approach for DFD based on sustainability. In this regard, a hybrid multi-attribute decision making (MADM) method integrating the regret theory (RT) and the entropy weighting method is firstly developed. To implement the proposed approach, an eight-criterion evaluation system 1
of schemes based on sustainability including the factors of disassembly energy consumption, disassembly accessibility, fastener ratio, toxic material proportion, material recovery rate, disassembly expense, production and use noise, and waste emissions, is established. To better describe the fuzziness of human thinking and to avoid information loss/distortion during information aggregation phases, the evaluation information given by experts is presented by our proposed interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs). The weight vector of index structure is determined by the entropy weighting method under the fuzzy environment. The RT is employed to get the final order of alternatives by considering and
of
quantitating both the risk attitude and the regret attitude of experts. To show the
ro
applicability of this study, a case study including four kinds of refrigerator schemes, is conducted to validate the proposed method. An extensive comparison with other
-p
recent and state of the art methods along with a sensitivity analysis of 13 experiments,
re
is executed to verify effectiveness and reliability of the proposed I2LI-RT method. Finally, the experimental results show that: 1) disassembly accessibility (C2), fastener
lP
ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on the scheme selection of DFD based on sustainability as those
na
attributes carry relatively the larger weights; 2) our proposed method outperforms
ur
other recent and state of the art methods and 3) the chosen scheme A1 is the winner in the majority of the sensitivity analysis cases (10 out of 13). At last but not least, the
Jo
main finding is to furnish a systematic and efficient decision support tool for sustainable performance evaluation of product schemes of DFD.
Keywords: Sustainability, Scheme selection, Design for disassembly (DFD), Multi-attribute decision making (MADM), Interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs), Regret theory (RT)
2
Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory Wenjie Wang a,b, Guangdong Tian a,b,c,*, Tongzhu Zhang d, Fangyi Li a,b, Amir M. Fathollahi-Fard e, Danqi Wang f,*, Noor H. Jabarullahg, Zhiwu Li h,i
a. Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan, 250061, China b. National Demonstration Center for Experimental Mechanical Engineering Education, Shandong
of
University, Jinan 250061, China
China
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c. School of Computer and Communication Engineering, Liaoning Shihua University, Fushun 113001,
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d. Automotive Standardization Research Institute, China Automotive Technology and Research Center, Tianjin 300300, China
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e. Department of Electrical Engineering, École de Technologie Supérieure, University of Quebec,
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1100 Notre-Dame St. W., Montréal, Canada f. State Key Laboratory of Automobile Simulation and Control, Jilin University, Changchun 130025,
na
China
g. Institute of Aviation Technology, University Kuala Lumpur, Selangor, Malaysia
ur
h. Institute of Systems Engineering, Macau University of Science and Technology, Taipa 999078, Macau, China
Jo
i. School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China Corresponding authors: G. D. Tian ([email protected]), D. Q. Wang ([email protected])
Abstract: Design for disassembly (DFD) is an essential design technique to consider the disassembly and recyclability of a product at the initial design stage. An efficient DFD technique provides the disassembling and recycling easily. However, the recent trends of disassembling and recycling are to consider the aspects of environmental and social sustainability. Due to shortage of energy and deterioration of the ecological environment, the sustainable production is an active research topic to use the economic and social benefits as the evaluation standard of a design scheme as well as its environmental characteristics. This paper provides a new approach for DFD based on sustainability. In this regard, a hybrid multi-attribute decision making (MADM) method integrating the regret theory (RT) and the entropy weighting method is firstly developed. To implement the proposed approach, an eight-criterion evaluation system 1
of schemes based on sustainability including the factors of disassembly energy consumption, disassembly accessibility, fastener ratio, toxic material proportion, material recovery rate, disassembly expense, production and use noise, and waste emissions, is established. To better describe the fuzziness of human thinking and to avoid information loss/distortion during information aggregation phases, the evaluation information given by experts is presented by our proposed interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs). The weight vector of index structure is determined by the entropy weighting method under the fuzzy environment. The RT is employed to get the final order of alternatives by considering and
of
quantitating both the risk attitude and the regret attitude of experts. To show the
ro
applicability of this study, a case study including four kinds of refrigerator schemes, is conducted to validate the proposed method. An extensive comparison with other
-p
recent and state of the art methods along with a sensitivity analysis of 13 experiments,
re
is executed to verify effectiveness and reliability of the proposed I2LI-RT method. Finally, the experimental results show that: 1) disassembly accessibility (C2), fastener
lP
ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on the scheme selection of DFD based on sustainability as those
na
attributes carry relatively the larger weights; 2) our proposed method outperforms
ur
other recent and state of the art methods and 3) the chosen scheme A1 is the winner in the majority of the sensitivity analysis cases (10 out of 13). At last but not least, the
Jo
main finding is to furnish a systematic and efficient decision support tool for sustainable performance evaluation of product schemes of DFD.
Keywords: Sustainability, Scheme selection, Design for disassembly (DFD), Multi-attribute decision making (MADM), Interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs), Regret theory (RT)
1. Introduction Nowadays, the rise in quantity and categories of obsolete products together with their improper disposing methods leads to heavy environmental pollution and huge waste of natural resources. This motivates a great pressure on maintaining sustainable development goals (Fathollahi-Fard et al., 2019a). In the summit of the Group of Twenty (G20), sustainability in global economy comes to be one of the most essential issues. Under such circumstances, some manufacturers choose to provide products 2
with green features or to establish a green supply chain (Yu et al., 2016; Qu et al., 2019). Design for disassembly (DFD) is a widely accepted efficient product design technique to produce a product that will be easily dismantled at the end of its lifecycle and therefore, the DFD can facilitate the product recovery process. A well-considered scheme of DFD not only guarantees a high productivity and a low energy consumption in disassembly processes, but also promotes the healthy development of industry (Fu et al., 2019; Fathollahi-Fard et al., 2019b). It goes without saying that some serious environmental problems such as global warming, stratospheric ozone
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depletion, and waste collection etc., promote manufacturing enterprises to consider
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the impact of a product design scheme on the environment (Yu and Lee, 2018). These reasons make the scheme selection of DFD based on sustainability, challengeable. To
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meet the sustainable development goals, this study aims to evaluate a set of product
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schemes of DFD and to rank them based on the criteria of sustainability with the use of a hybrid multi-attribute decision making (MADM) method.
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Scheme selection of DFD is usually studied as an MADM topic. To address various MADM problems, evaluation criteria and assessment methods are developed
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and proposed in the literature (Tian et al., 2018a). Many factors/criteria can directly
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effect on the evaluation performance of DFD schemes. For example, disassembly time and disassembly cost during the disassembly process are two typical core criteria
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in scheme evaluation and have been well-studied in the literature (Tian et al., 2019). However, various criteria and their complex relationships, makes the evaluation process, challengeable. To achieve a better performance in the scheme selection of DFD based on sustainability dimensions, a comprehensive evaluation scheme system to consider the environmental indicators, is indispensable and highly needed. Generally, the MADM methods aim to find out the best alternative or to order the alternatives from a finite number of schemes based on the evaluation information provided by relevant experts (Zhang et al., 2019). Due to the complexity of the environment and the fuzziness of human thinking, evaluation information may be ambiguous and may have some fuzziness to some extensions. Experts prefer the expression of their attitudes by using words/sentences instead of real numbers. To this end, this paper proposes the interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs) whose membership degree and non-membership degree are both denoted via interval 2-tuple linguistic terms, to better describe the fuzziness of environment 3
and avoid information loss in aggregation phases. On the other hand, it should be noted that a few scholars have successfully tried to introduce the RT initially proposed by Bell (1982) to solve various MADM problems (Qu et al., 2018; Peng et al., 2017). To the best of our knowledge, the RT, which has been used in recent decision making studies and whose effectiveness has been confirmed in real applications, is rarely studied in the area of scheme selection of DFD. In addition, some details are ignored in those existing MADM methods for scheme selection of DFD, e.g., environmental characteristics which should be emphatically considered to achieve the sustainability. With regards to aforementioned challenges and contributions, this paper
of
concentrates on a hybrid MADM method in the area of DFD scheme selection. The
ro
proposed hybrid method assists engineers in choosing the optimal scheme of DFD based on criteria of sustainability. Generally, this work is with the below four main
-p
contributions:
re
1) We propose a hybrid MADM method abbreviated as I2LI-RT to assess the performance of DFD schemes based on sustainability in a fuzzy environment.
lP
The qualitative evaluation information is processed by the proposed I2LIFNs to better describe the fuzziness and ambiguity. The main advantage of the
na
proposed method is to avoid information loss/distortion in information
ur
aggregation phases.
2) To evaluate the DFD schemes regarding the sustainability, some
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environmental indicators (i.e., toxic material proportion, material recovery rate, production noise and use noise, and waste emissions) are introduced and combined with disassembly indicators (i.e., disassembly energy consumption, disassembly accessibility, fastener ratio, and disassembly expense) to form an eight-criterion scheme evaluation system of DFD.
3) Schemes are ranked and the optimal scheme is determined through the well-accepted RT method. This method is rarely studied in the area of DFD scheme selection as far as we know. 4) The proposed MADM method furnishes a systematic and an efficient decision support tool for sustainable production to assess the performance of DFD schemes. The reminder of the paper is arranged as follows: Section 2 introduces a summary of the related works in this study area. Section 3 presents the proposed I2LI-RT method and its main steps. A refrigerator scheme evaluation example as a 4
real case study to show the applicability of our hybrid method, is presented in Section 4, followed by sensitivity analysis and a comparative study with other recent and state of the art methods. Finally, Section 5 concludes the results, findings and draws the future outlines.
Nomenclature Design for disassembly
MADM
Multi-attribute decision-making
RT
Regret theory
I2LIFSs
Interval 2-tuple linguistic intuitionistic fuzzy sets
I2LIFNs
Interval 2-tuple linguistic intuitionistic fuzzy numbers
G20
Group of twenty
FSs
Fuzzy sets
IFSs
Intuitionistic fuzzy sets
IVIFSs
Interval-valued intuitionistic fuzzy sets
IVLIFSs
Interval-valued linguistic intuitionistic fuzzy sets
IVLIFNs
Interval-valued linguistic intuitionistic fuzzy numbers
LCA
Life cycle assessment
DFA
Design for assembly
ur
na
lP
re
-p
ro
of
DFD
GC
Gray correlation Analytic hierarchy process
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AHP
TOPSIS
Technique for order preference by similarity to an ideal solution
ANP
Analytic network process
DOE
Design of experiment
LTS
Linguistic term set
T-WAA
2-tuple weighted arithmetic average operator
ST
An linguistic term set A linguistic term Symbolic translation Fuzzy number
/ /
Membership degree to number
/
Non-membership degree to number
/
Hesitation degree to number
of fuzzy set of fuzzy set
of fuzzy set 5
,
Hamming distance between two fuzzy sets
and
Entropy value about fuzzy set Utility function
∆
!
%#
Regret aversion coefficient
Entropy value of attribute C#
Weight of attribute C#
Membership degree utility value of alternative A under attribute
of
C#
Non-membership degree utility value of alternative A under
ℎ
#
+
#
A
- A
ro
-p
re
+* #
Rejoice value of membership degree of alternative A with
respect to that of alternative A
under attribute C#
Regret value of membership degree of alternative A
lP
ℎ* #
Normal distribution function
respect to that of alternative A
na
'(
attribute C#
under attribute C#
respect to that of alternative A
under attribute C#
Regret value of non-membership degree of alternative A with
respect to that of alternative A Weights vector to experts
Regret value of alternative A
under attribute C#
Rejoice value of alternative A
. A
Comprehensive perception value of alternative A
23
Distance closeness index of alternative A
/0 A 1
.0 A
with
Rejoice value of non-membership degree of alternative A with
ur
%#
,
Regret-rejoice function
Jo
$
!
Risk aversion coefficient
Amount of determinate information of alternative A GC closeness index of alternative A
Comprehensive perception value of alternative A
in the
comparison experiment
6
2. Literature review Since the contributions of this paper are four points as discussed in the introduction, the literature review is divided into four different but related streams including DFD, MADM methods, fuzzy theories and RT. Finally, the research gaps have been identified and our contributions to fill them are discussed. 2.1. DFD Contrary to the traditional design methods, the DFD is an efficient design
of
technique from the point of disassembly (Pan et al., 2001) and presents a remarkable application prospect. It is even regarded as a critical twenty-first century discipline
ro
that highlight a series of design rules (Bogue 2007).
-p
The idea of DFD has been used in various aspects in our daily life. For example,
re
regarding the study of Kondo et al. (2004), the DFD strategy was implemented in the life cycle assessment (LCA) for end-of-life electric home appliances. Regarding the
lP
importance of disassemblability design for end-of-life products, Viswanathan et al. (2006) described a model to research on the combinatorial configuration design
na
optimization problem with DFD technique. More recently, Favi et al. (2019)
ur
developed a time-based method and a software tool called Lean-DFD to assess the disassemblability of mechatronic products. To quantify the impacts of DFD on
Jo
buildings, Denis et al. (2018) put forward a new method called disassembly network analysis and their experimental results demonstrate its promising prospect. As one of important study in the literature review, Bogue (2007) pointed out that a successful DFD should entail three essential principles including the choice and adoption of raw materials, the design of product architecture, and the selection and the use of joints/fasteners. To assist engineers for determining appropriate fasteners of DFD, Ghazilla et al. (2014) presented a multi-criterion decision-making model by utilizing PROMETHEE method. Aguiar et al. (2017) developed a diagnostic tool to assess product recyclability during the product design phase where the amount, type and accessibility of fasteners and other factors were considered. To have one more step, an active disassembling fastener, as a DFD technology, was used in a LCA of end-of-life appliances recycling system on the basis of the waste input-output model (Nakamura et al., 2010). In recent researches on the DFD, the idea of design for assembly (DFA) is 7
considered. Soh et al. (2016) proposed a hybrid and systematic methodology that incorporated DFD and DFA and restrained it from the remanufacturing perspective. Based on rating factors, Shetty et al. (2015) presented a novel design tool for DFD/DFA to effectively test the ease of disassembly/assembly of products as a recent topic in the area of DFD techniques. 2.2. MADM methods Recently, there is a great deal of attention in the application of MADM methods for the scheme evaluation/selection related to the decision-making fields, such as gray
of
correlation (GC), analytic hierarchy process (AHP), technique for order preference by similarity to an ideal solution (TOPSIS), analytic network process (ANP), SAW,
ro
VIKOR and so on (Tian et al., 2018b).
-p
Although there are many MADM methods and each of them has a unique advantage, the hybrid MADM methods are recently proposed. For example, a group
re
of MADM methods including SAW, TOPSIS, and VIKOR, was used and
lP
compounded to assess the safety of seven Iranian airlines (Barak et al., 2018). Based on Delphi method, Hsu et al. (2017) used a hybrid MADM method integrating the
na
fuzzy AHP and the TOPSIS method to find key performances factors regarding the sustainability development of medium-sized enterprises. In addition, a new hybrid
ur
MADM model integrating ANP, DEMATEL-based ANP and GC method, was
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established to select optimal suppliers for addressing the supply chain management problem (Liou et al., 2016). Another new hybrid MADM technique consisting of ANP, TOPSIS and fuzzy max-min set methods, was introduced to assess several water transfer projects (Toosi et al., 2014). Most importantly, the hybrid MADM methods have been applied to disassembly evaluation field for product design, product recycle and so on (Feng et al., 2019a). For example, Yuan et al. (2019) used the GC technology to make a comprehensive evaluation of disassembly processes. Zhang et al. (2018) employed the AHP method on the basis of experts’ preferences for evaluating dismantling modes. Sabaghi et al. (2016) proposed a unique discriminant disassembly model to obtain disassemble ability index with the TOPSIS method and the design of experiment (DOE) method. As mentioned earlier, evaluation criteria are essential to the scheme selection of DFD and the hybrid MADM methods are needed. In this regard, Tang et al. (2004) offered a disassembly process evaluation model based on economic factors. On the 8
basis of Tang’s research, an environmental consequences criterion was added in Peeters et al. (2017) for an active disassembly evaluation. Recently, a five-criterion disassembly operation evaluation system including visibility, disassembly angle, number of tool’s changes and so on, was developed by Wang et al. (2016) with a software package designed by using Python programming language. Feng et al. (2019c) introduced three green indices of disassembly, i.e., disassembly cost, number of toxic parts and materials compatibility to determine a best scheme. At last but not least, the disassembly operation comport was selected as an evaluation index for product maintainability design (Zhu et al., 2020).
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2.3. Fuzzy theories
ro
Fuzziness is common in the literature review and can be encountered during the
-p
process of evaluating schemes of DFD. As one of important studies in the area of DFD, Tian et al. (2012) realized the quantitative evaluation for disassembly processes
re
through stochastic linear programming and maximum entropy theory. In another
lP
different research, Tian et al. (2018c) focused on fuzzy component quality and process cost to optimize disassembly sequences. With the perspective of disassembly,
na
Kazancoglu et al. (2018) utilized a fuzzy AHP approach to decide the criteria weights and employed a multi-objective optimization method to order disassembly tasks in
ur
addressing the disassembly line balancing problem under fuzzy environment.
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During the process of scheme selection in fuzzy environment, evaluation information on alternatives may be ambiguous and may have some fuzziness to some extent due to the complicacy of environments and the illegibility in human thinking, which is not suitable to be represented by exact numbers. For better expressing the uncertainty and fuzziness of information, several fuzzy theories are introduced, for example, fuzzy sets (FSs) (Zadeh 1965), intuitionistic fuzzy sets (IFSs) (Atanassov 1986) and interval-valued intuitionistic fuzzy sets (IVIFSs) (Atanassov et al., 1989). Compared with FSs, for IFSs, concepts of the membership degree and non-membership degree are added simultaneously and expressed in the form of crisp numbers. Different from IFSs, the membership degree and non-membership degree in IVIFSs are both denoted in the form of interval numbers instead of single crisp numbers, which is more expressive in describing uncertainty and fuzziness of evaluation information (Yang et al., 2020). However, the utilization of FSs, IFSs and IVIFSs may lead to the loss and distortion of information. According to Liu et al. 9
(2019), it will be more reasonable and convenient for experts to give their preference information by using linguistic forms sometimes. Later, Liu et al. (2017) put forward the concept of interval-valued linguistic intuitionistic fuzzy sets (IVLIFSs) which integrate the idea of linguistic variables and IVIFSs. As for IVLIFSs, membership degree and non-membership degree are both denoted by interval-valued linguistic terms to process imprecise information. However, although IVLIFSs can well address fuzziness under fuzzy environment, information loss may also occur in aggregation phases, which will mislead the evaluation results. The 2-tuple method proposed in Herrera et al. (2000), which can avoid information loss/distortion in information
of
aggregation phases, is suitable for processing information with linguistic forms.
ro
2.4. RT
-p
Although the RT proposed by Bell (1982) is an old theory, it is rarely studied in the area of MADM models. For example, Wang et al. (2020) proposed a
re
projection-based RT method for MADM problems under fuzzy sets environment.
lP
Gong at al. (2019) extended RT and applied it into the application for the stock market. The effectiveness of RT has been confirmed in real applications (Zhang et al., 2016).
na
Peng et al. (2019) combined RT with ELECTRE III method to establish a model that could effectively support the decision-making of new energy investment. Its basic
ur
idea is that, the decision makers not only focus on the results of the scheme that they
Jo
choose, but also pay attention to the comparison results between the scheme and other schemes that they do not choose in the decision making process, and avoid choosing the alternative that will make them feel regret (Qu et al., 2018; Peng et al., 2017). RT has the following three core characteristics: 1) it considers both the risk attitude and the regret attitude of decision makers; 2) it quantifies the psychological emotions of regret/rejoice of decision makers; 3) it involves few parameters and its calculation process is easy to understand. However, the adoption of RT is limited in scheme selection of DFD based on sustainability. As can be seen from the literature review, although there are many effective approaches to deal with the problem of scheme selection of DFD. Nevertheless, some aspects still be overlooked, e.g., environmental indicators, which have a significant impact on the assessment process for sustainable product design schemes, are rarely considered; RT, which has been successfully applied in recent decision making studies is limited to the evaluation of schemes of DFD. Besides, due to the complexity of the 10
environment and the fuzziness of human thinking, evaluation information may have some fuzziness to some extent and information loss may occur in aggregation phases. Therefore, the concept of interval 2-tuple linguistic intuitionistic fuzzy numbers is proposed and employed to present evaluation information. In this work, we will establish a comprehensive evaluation system of schemes of DFD based on sustainability in which disassembly and environmental characteristics of an alternative scheme are both considered. The weights vector of index structure is determined by the entropy weighting method. RT is utilized to obtain the final ranking
A hybrid MADM method I2LI-RT
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3.
of
of schemes of DFD to select the most sustainable one.
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3.1. Interval 2-tuple linguistic intuitionistic fuzzy sets/numbers (I2LIFSs/I2LIFNs)
re
Definition 3.1. Suppose X={x1, x2, …, xn}be the finite and nonempty universe of discourse. An interval 2-tuple linguistic intuitionistic fuzzy set (I2LIFS) is defined as:
2) J :;
,
D C
E
lP
E
= AB
,
D C
E
F,B
D C
E
,
D C
G C
E
,
D C
E
and 4) 0 ≤ ∆IS B
,
G C
G C
E
E
,
:;
,
E
G C
of set 45, which satisfy: 1)
Jo
degree to
:;
D C
:;
,
na
of set 45,
= AB
ur
:;
where
45 = 7<
E
F,B
,
I :;
G C
G C
E
E
,
>|
,
FH is the membership degree to G C
J :;
∈ N−0.5, 0.5 ; 3) G C
E
F + ∆IS B
∈ ?@
G C
E
E
,
,
FH is the non-membership ,
I :;
I :;
G C
E
≤
∈ 70,1, ⋯ , %@;
J :;
J :;
,
≤
I :;
F ≤ %. ST={s0, s1, ⋯,
st} is an linguistic term set (LTS) that is made up of a group of linguistic terms
(Herrera et al., 2000). ∆IS
that converts a 2-tuple to its equivalent numerical
al.,
degree
45
value is defined in Herrera et al. (2000). Similar to the definition of IVLIFNs (Liu et :;
2017), = AB
∆ U% − ∆IS B ∆ U% − ∆IS B
the D C
G C D C
E
E E
,
, ,
hesitation D C
G C D C
E
E E
F,B
G C
E
F − ∆IS B F − ∆IS B
,
G C D C
to G C
E E
E
, ,
FH
G C D C
of , E E
FV
FV.
set where ,
is
B B
expressed D C G C
E E
, ,
D C G C
E E
as
F= F=
Specially, if there exists only one element in set 45, then 45 degenerates into an 11
interval 2-tuple linguistic intuitionistic fuzzy number (I2LIFN) denoted simply as :; , :;
= BAB
D C
,
D C
F,B S,
Definition 3.2. Let X ={
YBAB
D C
E
,
D C
E
F,B
G C
E
YBAB
D ]
E
,
D ]
E
F,B
G ]
E
and
\; =
G C
X,
,
⋯,
G C
FH , AB
G C
E
FH , AB
,
G ]
E
FH , AB
,
G C
∆IS B ∆IS B
∆IS B S̃
̃ X
E
G C
E
G ]
,
G C
,
D C
E
,
G C
E
,
E
= N
= N
G ]
,
g , −0.3
E
E
F,
G C
d ( r%1, r%2 ) =
D ]
E
,
G C
E
D ]
the
D C
E
,
D C
D C
E
F,B
G C
E
,
G C
E
FHF Z
∈ ?[
D ]
E
,
D ]
E
F,B
G ]
E
,
G ]
E
FHF Z
∈ ?[
−
F,
E
e, N
−
^ , −0.5
G C
G ]
E
E
D ]
E
,
G ]
E
e, N
D ]
E
E
G C
E
,
D ]
F,
S , −0.5
S , 0.1
between sets 45 and \; is
G ]
E
Z+Z
= ∆IS B G ]
D ]
D C
E
,
E
E
D ]
,
,
G ]
E
,
Z+Z
D C
E
X , 0.2
G C
D ]
E
E
E
D ]
G ]
F
,
E
E
D C
−
E
G ]
D ]
D ]
E
−
D ]
F ,
G ]
F − ∆IS B
F.
between
F
E
E
D C
E
two
E
Z+ (1)
F,
,
,
D ]
ZF
E
E
= % − ∆IS B
E
distance
e
G ]
= ∆IS B
E
= ∆IS B
F − ∆IS B
,
E
= ∆IS B
= % − ∆IS B
f , 0.3
G C
45, \;
ro
D C
FHF.
E
Z+Z
hamming
G C
D C
=
E
=
E
,
D C
,
,
E
G ]
=%−
E
D C
E
F−
F,
I2LIFNs and
e is calculated by:
4 − 2.7 + 5.3 − 3.5 + 0.3 −1.1 + 0.5 − 2.2 + 0.2 − 0.3 + 1.7 − 2.2 = 0.258 4× 6
Definition 3.3. Let ? = 7 S ,
YBAB
Z+Z
F ,
E
F − ∆IS B
c , 0.3
,
E
G C
D C
-p
,
D ]
,
,
G C
example,
^, 0
E
E
,
F
= % − ∆IS B
For
G ]
D C
Jo
E
F
= ∆IS B
E
= ∆IS B
E
G ]
D C
E
−
ur
G C
E
E
−
,
,
lP
∆IS B
G C
E
na
D C
where
Z
D C
G C
E
re
S 45, \; = ^(_ ∑(aS BZ
F,B
D C
be the two I2LIFSs, the hamming distance
defined by:
D C
be the universe of discourse and 45 =
(}
,
D C
of
W=
E
F,B
G C
E
,
X, ⋯ , (@
G C
E
FH , AB
be the universe of discourse and 45 = D C
E
,
D C
F,B
E
be an I2LIFS. The entropy value of set 45 is expressed as: S 45 = ^(_ i ∑(aS 2% X − Z
G C
E
−
G C
E
X
Z −Z
D C
E
−
G C
D C
E
E
,
G C
X
E
Z +B
FHF Z D C
E
∈ ?[
X
F + 12
B
BAB
G C
E
F
X
(2)
Assuming that there are a group of I2LIFNs of size n, denoted as W = D k j
,
D k j
F,B
G k j
,
G k j
FH , AB
D k j
,
D k j
F,B
G k j
,
G k j
FHF, and their weights are marked
in vector l = mS , mX , ⋯ , m( n , then we aggregate them by using T-WAA operator defined in Herrera et al. (2000). The aggregation result is shown as:
D p j G p j
,
, ,
D p j G p j D p j G p j
G p j
,
G p j
FH , A
D p j
,
(
= ∆ uv m ∆IS B aS (
F = ∆ uv m ∆IS B
D p j
D k j
,
,B D k j
G p j
,
G p j
FHF
(3)
Fw
of
G p j
,
,B
G k j
,
G k j
Fw
ro
s r r r rB q
D p j
D p j
aS (
= ∆ uv m ∆IS B
,
-p
t r r r rB
,
aS (
re
where
D p j
F = ∆ uv m ∆IS B
lP
o = BA
aS
D k j
G k j
,
D k j G k j
Fw
Fw
na
3.2. Entropy weighting method
ur
The entropy weighting method is a widely-accepted technique to decide the
Jo
diverse attributes weights in solving MADM problems without any additional or subjective information (He et al., 2016). Basic procedures of the entropy weighting method based on the evaluation information in I2LIFN form are presented as follows: 1) establish the evaluation matrix A=(aij)n×m (i=1, 2, …, n; j=1, 2, …, m), where aij represents evaluation information of the i-th alternative under the j-th attribute; 2) calculate entropy values of attributes through Eq. (2) and 3) determine the weights of attributes by:
ωC = j
1 − EC j
∑ (1 − E ) m
d =1
(4)
Cd
3.3. RT The RT which initially originated from economics and psychology was first put forward by Bell (1982) and has been utilized in the decision making field. Its basic 13
idea is that the decision makers not only focus on the results of the scheme that they finally choose, but also pay attention to the comparison results between the scheme and others that they do not choose. Generally speaking, RT can be employed to quantitate the degree of regret and rejoice of the decision makers for each alternative scheme by pair comparisons. Three core functions, i.e., utility function v(x),
regret-rejoice function R(Δv) and comprehensive perception function .
, jointly
play an important role in the quantification process of RT. Therefore, main steps of RT can be divided into three parts. First of all, the evaluation information x will obtain its utility value through v(x). ,
D C
F,B
G C
,
values are obtained via:
G C
FH , AB
D C
,
D C
% =x
F,B
G C
with
,
G C
C
re
∆Dz U|}D ,~}D V C C
lP
∆Dz {|€G ,~€G •
where %
C
C
∆Dz U|€D ,~€D V
ur
na
% =x
C
v ( x) =
I2LIFN
FHF , its corresponding utility
∆Dz {|}G ,~}G • C
an
of
D C
information
ro
W = BAB
evaluation
-p
For
C
'
d
(5)
'
d
(6)
1 − e− β x
(7)
β
refers to the membership degree utility value and the bigger the better,
Jo
while %
is the non-membership degree utility value and the smaller the better.
is the utility function (Bell 1982; Peng et al., 2019), β is the risk aversion coefficient
with 0 < β < 1. The greater β is, the greater degree of risk aversion the decision maker will face. Note that the utility value varies greatly with respective to different
β values, as shown in Fig. 1. The value of β will affect the final results, and we will choose the commonly used β value in the literature as the final value of β. f(x)is the distribution
AB
D C
,
D C
F,B
function G C
,
G C
related
to
AB
D C
,
D C
F,B
G C
,
G C
FH
and
FH. Generally, when evaluation information is given in the
interval form, normal distribution is commonly considered. For an interval evaluation information •
z
,
z
,
i
,
i
‚, its normal distribution function '(
is defined 14
as follow:
=
∆Dz |‡z ,~‡z J∆Dz |‡i ,~‡i X
=
√X „
, ˆ=
e
∆Dz
UI
jD} i V i†i
‰2 , ‰2
I∆Dz Š
(8) ‰1 , ‰1
.
-p
ro
of
where
'(
S
Fig. 1. The utility function v(x)
re
And then, regret values and rejoice values will be obtained through R(Δv). For a
D k! Œ
,
D k! Œ
V,U
G k! Œ
,
G k! Œ
V• , ‹U
D k! Œ
,
na
U‹U
lP
group of evaluation information on attribute Cj of alternative Ai denoted as ̃ # = D k! Œ
V,U
G k! Œ
,
G k! Œ
V•V, its corresponding regret
Jo
ur
value and rejoice value are obtained by the following: +
ℎ
+* # = Ž
ℎ* # = Ž
+ ℎ
where +
#
and ℎ
#
# #
=• =•
#
#
=+ =ℎ 0,
#
#
%#−%
%#−% 0,
0,
%
#
++ +ℎ
#
#
%# ≥% #
#
(9) (10) #
,% # < %
,% # ≥ %
%# <% %# <%
# #
− % # ,% # ≥ %
% # − % # ,% # < % 0, %# ≥% #
R ( ∆v) = 1− exp ( −γ ×∆v)
#
#
#
#
(11)
(12)
(13)
(14) (15)
represent the regret value and rejoice value of alternative A
with respect to that of alternative A
under attribute C# , respectively. ℎ* # and +* #
represent the rejoice value and regret value of membership degree of alternative A
15
with respect to that of alternative A
under attribute C# , respectively; ℎ
and +
#
are positive numbers and the bigger the better, while +* # and +
#
#
represent the rejoice value and regret value of non-membership degree of alternative
A with respect to that of alternative A ℎ* # and ℎ
#
under attribute C# , respectively. Generally, ∆
are negative numbers and the bigger the better.
is the regret-rejoice function
and parameter Δv represents the difference between two utility values and γ∈(0, +∞) is the regret aversion coefficient (Bell 1982; Chorus et al., 2012). Note that the regret-rejoice value also ranges widely with respective to different γ values, as shown
ur
na
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R( v)
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ro
used γ value in the literature as the final value of γ.
of
in Fig. 2. The value of γ will also affect the final results, and we choose the commonly
∆
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Finally, the comprehensive perception function . Fig. 2. The regret-rejoice function
is used to find
comprehensive perception value of each alternative scheme through ( 4 = ∑‘ #aS m ! ∑ aS +
.
- A
=’
( = ∑‘ #aS m ! ∑ aS ℎ
“ E I“ G “ G I“ D
+ 1−’
#
#
” E I” D ” G I” D
(16) (17) (18)
where R(Ai) and H(Ai) represent the regret value and the rejoice value of alternative
Ai. m
!
that represents the weight of attribute C# is determined by the entropy
weighting method.
J
= max
A ,
I
= min
A , - J = max - A
and
- I = min - A . ’ is the balance factor and ranges from zero to one, and to avoid
the loss of generality, the value of ’ is set as 0.5 in this paper.
3.4. Integrated assessment process for scheme selection of DFD 16
The main steps of our proposed I2LI-RT method for scheme selection of DFD based on sustainability are presented as follows. Note that the general structure of I2LI-RT method is illustrated in Fig. 3 and environmental indicators and disassembly indicators are considered in assessment attributes. First of all, we give the following settings: there exist n alternatives marked in {A1, …, Ai, …, An} that have m attributes marked in {C1, …, Cj, …, Cm} for the decision maker to determine; a group of e experts marked in {E1, …, Ek, …, Ee} give their evaluation information
#
š
on the
i-th alternative under the j-th attribute; the weights vector to experts is , = satisfying
∑ek=1 λk = 1 and 0 ≤ › ≤ 1.
of
n
Jo
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na
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ro
›S , ›X , … , ›•
Fig. 3. The framework of the proposed hybrid MADM method I2LI-RT
Step 1. Decide an LTS ST for scheme selection of DFD, and then obtain the initial
evaluation matrices ž Ÿ = B š
U‹
D !
š
,
G !
š
from set ST.
•,‹
D !
š
,
G !
š
#
š
F
(ב
.
#
š
•V and the elements in
is given in the form of #
š
#
š
=
are linguistic terms selected
17
Step 2. Transform ž Ÿ
š
into standardization matrices ž Ÿ = B
following standardization strategy: #
=¡
U‹
D !
,
G !
B
•=‹
#
š
D !
F
š
,
G !
š
•,‹
D !
,
G !
•=‹
¢ ∈ £J D !
š
,
G !
#
š
F
(ב
through the
19
•V ¢ ∈ £I
where £J indicates the index set where corresponding attributes are benefit
attributes; £I indicates the index set where corresponding attributes are cost attributes.
Step 3. Convert the evaluation information in ž Ÿ into 2-tuples by function ∆ ∙ defined in Herrera et al. (2000). Then obtain I2LIFN matrices ž Ÿ = B ̃ # F ̃#
(ב
.
based on ž Ÿ and the
of
Step 4. Establish the comprehensive matrix ž =
(ב
ro
weights vector , assigned to the experts, where ̃ # is obtained by Eq. (3). the weights m
!
-p
Step 5. Entropy values of various attributes are obtained via Eq. (2) and then obtain via Eq. (4).
based on ž. Elements in T are in
re
Step 6. Establish the utility matrix ¦ = % #
(ב
lP
the form of % # = % *# , % # , where % *# and % # are calculated by Eqs. (5)–(8).
na
Step 7.1. Calculate the membership degree regret matrices §¨ = + membership degree rejoice matrices ª¨ = ℎ
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and (12);
©
©
# (×(
# (×( and
under attribute Cj via Eqs. (11)
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Step 7.2. Calculate the non-membership degree regret matrices §«¨ = + the non-membership degree rejoice matrices ª«¨ = ℎ Eqs. (13) and (14);
Step 7.3. Establish the regret matrices §¨ = + ª¨ = ℎ
# (×(
the
# (×(
# (×(
# (×( and
under attribute Cj via
and the rejoice matrices
under attribute Cj by Eqs. (9) and (10);
Step 8. Calculate the regret value
A
alternative Ai by adopting Eq. (16) and (17);
and the rejoice value - A
of each
Step 9. For each alternative A , find its associated comprehensive perception value . A
by Eq. (18).
Step 10. Order the alternatives according to . A
and select the optimal alternative
that has the highest value.
18
4. Experimental results and discussions 4.1. Case study Sustainable production and assessment have been essential for manufacturers and policy makers. In the summit of G20, sustainability is even regarded as one of the most crucial issues. Refrigerators are one of the common household appliances in China. According to the media reported, the number of waste refrigerators in different provinces and cities was increasing in the past decades, which brought great burdens to the environment protection and exacerbated the greenhouse effect. Exactly, China
of
increased its refrigerator capacity with an annual growth rate of 8.2% and generated
ro
89.92 million refrigerators in 2015 (Xiao et al., 2016). Also, highly valued materials or components in waste refrigerators have stimulated the unregulated recycling
-p
activities, which leads to severe pollution on the local soil and groundwater (Tian et
re
al., 2018b).
Great efforts have been made in addressing this tricky problem. In recent years,
lP
China has drawn up a series of policies and regulations to require manufacturers to
na
recycle obsolete refrigerators to reduce their life-cycle environmental impacts. Besides, some advanced and sophisticated disassembly technologies used for
ur
recovering the materials from obsolete refrigerators are published in articles and some of those technologies are introduced in real applications. Nevertheless, deciding how
Jo
to evaluate the refrigerators schemes of DFD based on sustainability remains to be resolved. Therefore, we evaluate four kinds of refrigerator alternatives via the proposed I2LI-RT method and a designed eight-criterion scheme evaluation system. In the case study, four refrigerator design schemes (namely A1-A4) are obtained from Tian et al. (2018b), Liu (2004) and Guo et al. (2015), and detailed parameters of the four refrigerator design schemes are shown in Table 1. To establish a comprehensive evaluation system to assess each alternative for sustainability objectively, original data are collected from Guo et al. (2015) and Tian et al. (2018b) and questionnaires done by experts with professional knowledge and rich working experience in the DFD field, e.g., scholars of university and supervisors of enterprise (Safaeian et al., 2019). Finally, a comprehensive evaluation system with eight core criteria including disassembly and environmental characteristics, i.e., disassembly energy consumption (kW·h) (C1), disassembly accessibility (C2), fastener ratio (C3), 19
toxic material proportion (C4), material recovery rate (C5), disassembly expense (Yuan) (C6), production and use noise (dB) (C7), and waste emissions (mg) (C8) is established. The illustration of those criteria is presented in Fig. 4, where cost criteria are marked in brown and benefit criteria are marked in green, and discussion of those criteria is present in Section 4.5. The evaluation LTS is chosen as: S7= {s0 =Extremely Terrible, s1 =Terrible, s2 =Medium Terrible, s3 = Ordinary, s4 = Medium Fine, s5 = Fine, s6 = Extremely Fine}. Three additional experts (namely E1, E2 and E3) are invited to give their evaluation information based on the seven-level LTS and their evaluation results on the four alternatives are shown in Tables 2-4. In general, the weights vector S S S n
assigned to experts is set to , = B , , F .
Jo
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g g g
Fig. 4. Comprehensive evaluation system of scheme of DFD based on sustainability
Table 1. Detailed parameters of the four refrigerator design schemes C1(kW·h)
C2
C3(%)
C4(%)
C5(%)
C6(/Yuan)
C7(dB)
C8(mg)
A1
0.53
0.8
0.5
1.4
40
45
110
16.1040
A2
0.62
0.7
0.6
1.4
40
50
108
16.1040
A3
0.68
0.6
0.7
1.5
42
55
112
13.0115
A4
0.52
0.5
0.3
0.1
35
51
105
13.9416 20
š
A1 A2 A3 A4
A4
([s2, s2],
([s1, s2],
([s1, s2],
[s0, s0])
[s3, s4])
[s4, s4])
([s5, s5],
([s0, s0],
([s0, s1],
[s2, s4])
[s0, s1])
[s4, s6])
[s3, s5])
([s1, s3],
([s4, s5],
([s1, s1],
[s2, s3])
[s0, s0])
([s0, s0], [s6, s6])
C6
([s4, s4],
C7
C8
([s1, s1],
([s0, s1],
([s1, s2],
[s1, s2])
[s3, s5])
[s2, s4])
[s4, s4])
([s3, s5],
([s0, s2],
([s0, s1],
([s1, s1],
[s1, s1])
[s4, s4])
[s2, s5])
[s3, s5])
([s0, s2],
([s5, s6],
([s2, s2],
([s0, s3],
([s0, s0],
[s3, s5])
[s2, s4])
[s0, s0])
[s2, s4])
[s1, s3])
[s3, s6])
([s3, s4],
([s0, s0],
([s0, s0],
([s3, s4],
([s1, s2],
([s0, s0],
([s0, s1],
[s0, s2])
[s4, s5])
[s5, s6])
[s1, s2])
[s3, s4])
[s4, s6])
[s4, s5])
C2
C3
C4
C5
([s1, s1],
([s6, s6],
([s0, s0],
([s1, s1],
([s4, s4],
of
C1
C6
C7
C8
([s0, s1],
([s0, s0],
[s4, s5])
[s0, s0])
[s5, s6])
[s4, s5])
[s1, s1])
[s4, s5])
[s5, s5])
[s5, s6])
([s3, s5],
([s0, s1],
([s2, s2],
([s2, s4],
([s0, s2],
([s1, s2],
([s0, s1],
[s4, s4])
[s1, s1])
[s3, s5])
[s3, s4])
[s0, s2])
[s3, s4])
[s4, s4])
[s4, s5])
([s0, s1],
([s4, s4],
([s1, s1],
([s2, s2],
([s3, s4],
([s1, s1],
([s0, s2],
([s0, s1],
[s4, s5])
[s0, s1])
[s4, s5])
[s4, s4])
[s0, s1])
[s4, s4])
[s2, s4])
[s4, s4])
([s1, s2],
([s3, s4],
([s1, s1],
([s0, s2],
([s4, s5],
([s1, s1],
([s1, s1],
([s0, s1],
[s3, s4])
[s0, s2])
[s4, s4])
[s4, s4])
[s1, s1])
[s4, s5])
[s4, s4])
[s3, s5])
re
-p
([s1, s1],
([s1, s2],
ro
A4
A3
[s3, s5])
C5
lP
A3
A2
([s5, s6],
C4
na
š
A2
A1
([s0, s1],
C3
Table 3. The original evaluation information given by expert E2
A1
ž®
C2
Table 4. The original evaluation information given by expert E3 š
C1 ([s0, s0],
C2
C3
C4
C5
C6
C7
C8
([s4, s6],
([s2, s2],
([s1, s2],
([s5, s5],
([s1, s1],
([s1, s1],
([s0, s1],
ur
ž-
C1
Jo
ž¬
Table 2. The original evaluation information given by expert E1
([s1, s1],
[s4, s5])
[s0, s1])
[s4, s5])
[s4, s5])
[s1, s2])
[s4, s4])
[s4, s4])
[s4, s5])
([s0, s1],
([s3, s5],
([s1, s1],
([s1, s2],
([s4, s4],
([s0, s1],
([s2, s2],
([s2, s3],
[s3, s4])
[s0, s0])
[s3, s4])
[s3, s4])
[s1, s1])
[s4, s4])
[s3, s3])
[s3, s3])
([s0, s1],
([s4, s4],
([s0, s0],
([s2, s2],
([s3, s4],
([s1, s2],
([s1, s2],
([s1, s2],
[s3, s5])
[s0, s2])
[s3, s5])
[s3, s3])
[s1, s2])
[s3, s4])
[s3, s3])
[s4, s4])
[s5, s6])
[s0, s0])
[s4, s4])
[s4, s4])
[s0, s1])
[s4, s5])
[s3, s5])
[s4, s4])
([s1, s1],
([s5, s5],
([s0, s1],
([s4, s4],
([s1, s1],
([s1, s1],
([s1, s1],
4.2. Results obtained by proposed I2LI-RT After reviewing the existing studies on RT,
is set to 0.02 and
is set to 0.3.
According to the main steps on the I2LI-RT method mentioned in Section 4.2, we get the calculation results step by step. Step 2. Standardization matrix ž ¬ is shown in Table 5 as an example.
21
Table 5. The standardization matrix ž ¬
ž¬
C1
A1 A2 A3 A4
C2
C3
C4
C5
C6
C7
C8
([s3, s5],
([s5, s6],
([s3, s4],
([s4, s4],
([s4, s4],
([s3, s5],
([s2, s4],
([s4, s4],
[s0, s1])
[s0, s0])
[s2, s2])
[s1, s2])
[s1, s2])
[s1, s1])
[s0, s1])
[s1, s2])
([s2, s4],
([s5, s5],
([s4, s6],
([s3, s5],
([s3, s5],
([s4, s4],
([s2, s5],
([s3, s5],
[s1, s2])
[s0, s1])
[s0, s0])
[s0, s1])
[s1, s1])
[s0, s2])
[s0, s1])
[s1, s1])
([s2, s3],
([s4, s5],
([s3, s5],
([s2, s4],
([s5, s6],
([s2, s4],
([s1, s3],
([s3, s6],
[s1, s3])
[s0, s0])
[s1, s1])
[s0, s2])
[s0, s0])
[s2, s2])
[s0, s3])
[s0, s0])
([s6, s6],
([s3, s4],
([s4, s5],
([s5, s6],
([s3, s4],
([s3, s4],
([s4, s6],
([s4, s5],
[s0, s0])
[s0, s2])
[s0, s0])
[s0, s0])
[s1, s2])
[s1, s2])
[s0, s0])
[s0, s1])
A3 A4
C4
C5
C6
C7
C8
([(s3, 0), (s5, 0)],
([(s5, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s4, 0)],
[(s0, 0), (s1, 0)])
[(s0, 0), (s0, 0)])
[(s2, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
([(s4, 0), (s4, 0)], [(s1, 0), (s2, 0)])
([(s3, 0), (s5, 0)], [(s1, 0), (s1, 0)])
([(s2, 0), (s4, 0)],
([(s4, 0), (s4, 0)],
[(s0, 0), (s1, 0)])
[(s1, 0), (s2, 0)])
([(s2, 0), (s4, 0)],
([(s5, 0), (s5, 0)],
([(s4, 0), (s6, 0)],
([(s3, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
([(s4, 0), (s4, 0)],
([(s2, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
[(s1, 0), (s2, 0)])
[(s0, 0), (s1, 0)])
[(s0, 0), (s0, 0)])
[(s0, 0), (s1,0)])
[(s1, 0), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 0), (s1, 0)])
[(s1, 0), (s1, 0)])
([(s2, 0), (s3, 0)],
([(s4, 0), (s5, 0)],
([(s3, 0), (s5, 0)],
([(s2, 0), (s4, 0)],
([(s5, 0), (s6, 0)],
([(s2, 0), (s4, 0)],
([(s1, 0), (s3, 0)],
([(s3, 0), (s6, 0)],
[(s1, 0), (s3, 0)])
[(s0, 0), (s0, 0)])
[(s1, 0), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 0), (s0, 0)])
[(s2, 0), (s2, 0)])
[(s0, 0), (s3, 0)])
[(s0, 0), (s0, 0)])
([(s6, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s5, 0)],
([(s5, 0), (s6, 0)],
([(s3, 0), (s4, 0)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s6, 0)],
([(s4, 0), (s5, 0)],
[(s0, 0), (s0, 0)])
[(s0, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
[(s1, 0), (s2, 0)])
[(s0, 0), (s0, 0)])
[(s0, 0), (s1, 0)])
-p
C3
re
A2
C2
lP
A1
C1
na
ž¬
ro
Table 6. I2LIFN matrix ž ¬
of
Step 3. I2LIFN matrix ž ¬ is shown in Table 6 as an example.
[(s0, 0), (s0, 0)])
[(s0,0), (s0, 0)])
ur
Step 4. The comprehensive matrix ž is shown in Table 7.
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Step 5. The entropy values of eight attributes are presented in Table 8 and their corresponding normalized weights are presented in Table 9. Based on the results, we get that disassembly accessibility (C2), fastener ratio (C3), disassembly waste emissions (C8), and disassembly energy consumption (C1) have a large impact on scheme selection of DFD based on sustainability since those attributes carry the relatively larger weights. Table 8. The entropy values of eight attributes E(C# )
C1
C2
C3
C4
C5
C6
C7
C8
0.3711
0.2847
0.3480
0.4105
0.3881
0.4066
0.4360
0.3611
Table 9. The weights of eight attributes obtained by entropy weighting method m
!
C1
C2
C3
C4
C5
C6
C7
C8
0.1259
0.1432
0.1306
0.1180
0.1225
0.1188
0.1129
0.1279
22
Step 6. The utility matrix ¦ = % #
(ב
is shown in Table 10.
Table 10. The utility matrix
¦
C1
C2
C3
C4
C5
C6
C7
C8
A1
(4.4430, 0.4961)
(5.1940, 0)
(4.1395, 1.3157)
(3.9870, 1.3120)
(4.1509, 0.9873)
(4.1392, 0.8242)
(3.8334, 0.8242)
(4.2918, 0.6603)
A2
(3.6799, 1.3120)
(4.4434, 0.6603)
(4.2911, 0.4961)
(3.8334, 0.9873)
(3.5255, 1.1498)
(3.6801, 0.9869)
(3.6799, 0.9873)
(4.1392, 0.8242)
A3
(3.5709, 0.9869)
(3.9867, 0.1659)
(3.8334, 0.9901)
(3.3709, 1.4735)
(4.1395, 0.4961)
(3.5258, 1.1500)
(2.5893, 1.4730)
(3.6799, 0.9873)
A4
(4.2916, 0.6603)
(3.5258, 0.9863)
(3.9867, 0.3322)
(3.9870, 0.9873)
(3.6799, 1.3120)
(3.6799, 1.3120)
(3.8337, 0.8242)
(3.9867, 0.8239)
Step 7.1. The membership degree regret matrix §¬ and the membership degree ©
rejoice matrix ª¬ under attribute CS are shown in Table 11 as an example. ©
Table 11. The membership degree regret matrix §¬ and the membership degree rejoice matrix ª¬ under attribute C1 Regret matrix §¬ A2
A3
A4
A1
©
©
A2
A3
A4
0
0.2046
0.2750
0.0444
0
0
0.0885
0
-p
A1
Rejoice matrix ª¬
ro
©
C1
of
©
0
0
0
0
A2
-0.2573
0
0
-0.2014
A3
-0.3794
-0.0971
0
-0.3181
0
0
0
0
A4
-0.0465
0
0
0
0
0.1677
0.2413
0
lP
re
A1
Step 7.2. The non-membership degree regret matrix §«¬ and the non-membership
na
degree rejoice matrix ª«¬ under attribute CS are shown in Table 12 as an example.
ur
Table 12. The non-membership degree regret matrix §«¬ and the non-membership degree rejoice matrix ª«¬ under attribute C1 Regret matrix §«¬
Jo
C1
A1
A2
A3
A4
A1
0
0
0
0
A2
-0.2773
0
-0.1025
A3
-0.1586
0
A4
-0.0505
0
A1
Rejoice matrix ª«¬ A2
A3
A4
0
0.2171
0.1369
0.0481
-0.2159
0
0
0
0
0
-0.1029
0
0.0929
0
0
0
0
0
0.1776
0.0933
0
Step 7.3. Regret matrix §¬ and rejoice matrix ª¬ under attribute CS are shown in Table 13 as an example.
Table 13. Regret matrix §¬ and rejoice matrix ª¬ under attribute C1
C1 A1
Regret matrix §¬ A2
A3
A4
A1
Rejoice matrix ª¬ A2
A3
A4
A1
0
0
0
0
0
0.4218
0.4119
0.0925
A2
-0.5346
0
-0.1025
-0.4174
0
0
0.0885
0
A3
-0.5380
-0.0971
0
-0.4210
0
0.0929
0
0
A4
-0.0970
0
0
0
0
0.3452
0.3347
0 23
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f
Table 7
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The comprehensive matrix
C2
C3
C4
C5
C6
C7
C8
([(s4, 0), (s5, 1/3)],
([(s5, 0), (s6, 0)],
([(s4, 0), (s5, -1/3)],
([(s4, 0), (s4, 1/3)],
([(s4, 1/3), (s4, 1/3)],
([(s4, -1/3), (s5, 0)],
([(s3, 1/3), (s5, -1/3)],
([(s4, 1/3), (s5, -1/3)],
[(s0, 1/3), (s1, -1/3)])
[(s0, 0), (s0, 0)])
[(s1, 1/3), (s1, 1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s1, 0)])
[(s1, -1/3), (s1, 0)])
[(s0, 1/3), (s1, 0)])
([(s3, 1/3), (s4, 1/3)],
([(s4, 1/3), (s5, 0)],
([(s4, -1/3), (s5, 1/3)],
([(s3, 1/3), (s5, -1/3)],
([(s3, 0), (s4, 1/3)],
([(s4, -1/3), (s4, 0)],
([(s3, 1/3), (s4, 1/3)],
([(s4, -1/3), (s5, 0)],
[(s1, 0), (s2, -1/3)])
[(s0, 1/3), (s1, 0)])
[(s0, 1/3), (s1, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s2, -1/3)])
[(s0, 1/3), (s2, -1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, -1/3), (s1, 0)])
([(s3, 0), (s4, 0)],
([(s4, -1/3), (s5, -1/3)],
([(s3, 1/3), (s5, -1/3)],
([(s3, 0), (s4, 0)],
([(s4, 0), (s5, -1/3)],
([(s3, 1/3), (s4, 0)],
([(s2, 0), (s3, 1/3)],
([(s3, 1/3), (s4, 1/3)],
[(s0, 1/3), (s2, -1/3)])
[(s0, 0), (s0, 1/3)])
[(s1, 0), (s1, 0)])
[(s1, 0), (s2, 0)])
[(s0, 1/3), (s1, -1/3)])
[(s1, 0), (s1, 1/3)])
[(s1, -1/3), (s2, 1/3)])
[(s1, -1/3), (s1, 1/3)])
([(s4, 0), (s5, 0)],
([(s3, 1/3), (s4, 0)],
([(s3, -1/3), (s5, -1/3)],
([(s4, 0), (s4, 1/3)],
([(s3, 1/3), (s4, 1/3)],
([(s3, 1/3), (s4, 1/3)],
([(s4, -1/3), (s4, 1/3)],
([(s4, -1/3), (s5, -1/3)],
[(s0, 1/3), (s1, 0)])
[(s0, 0), (s2, 0)])
[(s0, 1/3), (s0, 1/3)])
[(s1, -1/3), (s1, 1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, 0), (s2, -1/3)])
[(s1, -1/3), (s1, 0)])
[(s0, 1/3), (s1, 1/3)])
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C1
24
Step 8. Regret values presented as follows:
A4
A3
A2
A1
A
and rejoice values - A
of each alternative A are
AS = −0.1443, - AS = 0.6293;
AX = −0.3874, - AX = 0.3030; Ag = −0.7686, - Ag = 0.2006; A^ = −0.4629, - A^ = 0.3007.
Step 9. The comprehensive perception values . A
for each alternative A are
shown as follows:
of
. AS = 0.5000, . AX = −0.0753, . Ag = −0.5000, . A^ = −0.1385.
Step 10. Therefore, we find the final rank: AS > AX > A^ > Ag . That is, AS is the
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optimal design scheme according to the I2LI-RT method, followed by AX , A^ and
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Ag .
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4.3. Comparative studies with other state of art methods
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a. Comparison with the information entropy measure In this subsection, we extend the information entropy measure to I2LIFNs, and
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the case study will be solved again by the new method called I2LI-IEM for short.
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According to Zhao et al. (2016), alternatives are ranked by comparing the amount of determinate information. We calculate the amount of determinate information of each alternative and
obtain: /0 AS = 0.6894 ,
/0 AX = 0.6027 ,
/0 Ag = 0.5714 ,
0.5833. Therefore, we have the following rank: AS > AX > A^ > Ag .
/ 0 A^ =
b. Comparison with the GC method In this subsection, we develop the GC method to I2LIFNs. The case study will be solved again by the new fuzzy GC method called I2LI-GC for short. Some adaptive approaches based on I2LI-GC and our experimental conditions are adopted.
We calculate the GC closeness index 1 for each alternative and get: 1S =
0.3935,
1X = 0.4993,
1g = 0.5952,
rank: AS > AX > A^ > Ag .
1^ = 0.5008. So, we have the following
c. Comparison with the TOPSIS method 25
Hu et al. (2007) proposed the TOPSIS method for solving an MADM problem with fuzzy evaluation information. In this subsection, we extend this method to I2LIFNs, and the case study will be solved again by the new fuzzy TOPSIS method called I2LI-TOPSIS for short.
We work out the distance closeness index 23 for each alternative and obtain:
23z = 0.2649 , 23i = 0.2701 , 23³ = 0.5278 , 23´ = 0.4641 . So, we have the following rank: AS > AX > A^ > Ag
d. Comparison with IVLIFNs and RT
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I2LIFNs can be regarded as a variant of IVLIFNs (Liu et al., 2017), so in this comparison experiment, we decide to adopt the IVLIFNs to represent and process the
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evaluation information. Furthermore, to confirm the effectiveness of the I2LI-RT
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method, RT is also used to decide the final order and the best alternative. Note that we call this integrated method IVLI-RT for short.
and get: . 0 AS =
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We compute the comprehensive perception values . 0 A
0.5000, . 0 AX = −0.2931, . 0 Ag = −0.4773, . 0 A^ = −0.0692. So, we have
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the following rank: AS > A^ > AX > Ag
e. Discussions between I2LI-RT and the comparative studies
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For ease of analysis, we put all the ranking results together obtained by the five
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methods, i.e., I2LI-RT, I2LI-IEM, I2LI-GC, I2LI-TOPSIS and IVLI-RT, in Table 14. It can be seen that A1 is the optimal scheme based on the I2LI-RT method or the rest four comparison methods. Thus, the effectiveness of the I2LI-RT method is verified. The ranking results of I2LI-RT, I2LI-IEM, I2LI-GC and I2LI-TOPSIS methods are mainly accordant, which demonstrates the combination of I2LIFNs and the RT is rational and practicable to conduct scheme selection of DFD based on sustainability.
Table 14. Ranking results obtained by I2LI-RT method and four comparison methods I2LI-RT
. A
I2LI-IEM
Rank
A1
0.5000
1
A2
-0.0753
A3 A4
/0 A
I2LI-GC
Rank
I2LI-TOPSIS
1
Rank
23
Rank
0.6894
1
0.3935
1
0.2649
1
2
0.6027
2
0.4993
2
0.2701
-0.5000
4
0.5714
4
0.5952
4
-0.1385
3
0.5833
3
0.5008
3
IVLI-RT
.0 A
Rank
0.5000
1
2
-0.2931
3
0.5278
4
-0.4743
4
0.4641
3
-0.0692
2
26
However, some differences exist among those ranking results. For the I2LI-IEM method, although the ranking result is the same as that obtained by I2LI-RT, I2LI-IEM cannot tell how well or bad an alternative scheme is. In our proposed I2LI-RT, the worse the scheme is, the greater the probability that its corresponding value becomes a small negative number. Moreover, a set of reasonable parameters in I2LI-RT can help enlarge the difference gap between schemes. For the I2LI-GC method, it does not determine the better one between the schemes A2 and A4 due to that their corresponding gray closeness indices are relatively close, while our I2LI-RT method can do it. This is due to the fact that the GC method cannot report the distance among information sequences and the RT essentially has the property of
of
distance comparison. For the I2LI-TOPSIS method, it can be seen that 23z is
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approximately the same as 23i . In fact, A1 is not slightly better than A2, thus using
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I2LI-TOPSIS may not clearly reflect actual conditions; while the proposed I2LI-RT
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method can have a relatively strong ability to resolution. This is because that
information sequences.
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regarding distance as the unique measure will not tell the situation changes among
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As Table 14 demonstrates, A2 ranks before A4 and A3 ranks after A4 using the IVLI-RT method, while A2 ranks after A4 and A3 ranks before A4 using the rest four
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methods. The explanation for the ranking inconsistences mainly depends on the features of the comparison methods. The IVLI-RT method adopts IVLIFNs to
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evaluate the performance of the four alternative schemes. However, the proposed I2LI-RT method uses I2LIFNs for assessing those schemes, which can not only capture the vagueness and uncertainty of evaluation information given by experts, but also reduce information loss/distortion in the aggregation phase. 4.4.Sensitivity analysis The sensitivity analysis is also conducted to measure the robustness of I2LI-RT method by adjusting the attributes weights (Feng et al., 2019b). Considering the amount of attributes used in the case study, thirteen experiments are designed to record the final rank and the experimental outcome is shown in Table 15.
Table 15. Experimental outcome of sensitivity analysis for thirteen experiments Expt
Weights
Comprehensive perception values . A
Rank 27
2 3 4 5 6 7 8 9 10 11 12
m ³ =0.825, m m ´ =0.825, m m ¶ =0.825, m m · =0.825, m
m m m m
z, ³I
zI ¶ zI ³ zI zI
-0.4463
-0.5000
A^
0.2580
1>4>2>3
0.5000
-0.0232
-0.0512
-0.5000
1>2>3>4
=0.025
-0.3280
0.5000
-0.5000
0.3483
2>4>1>3
=0.025
0.3237
0.3680
-0.5000
0.5000
4>2>1>3
=0.025 µ
=0.025 µ
zI ³, ¶I µ zI ´, ·I
0.3166
-0.4846
0.4963
-0.5000
3>1>2>4
=0.025 µ
0.5000
-0.1026
-0.5000
-0.4178
1>2>4>3
=0.025
0.5000
0.2588
-0.5000
0.4263
1>4>2>3
0.5000
0.1113
-0.5000
-0.0260
1>2>4>3
0.5000
-0.0610
-0.5000
-0.0922
1>2>4>3
=0.075
0.5000
-0.1411
-0.5000
-0.1686
1>2>4>3
=0.155
0.5000
-0.0439
-0.5000
-0.0631
1>2>4>3
=0.050 µ
0.5000
-0.0062
-0.5000
-0.0314
1>2>4>3
0.5000
-0.1309
-0.5000
-0.1729
1>2>4>3
zI ¶, ¸I
zI ·, µ
m µ =0.825, m zI
0.5000
Ag
zI i, ´I µ
m ¸ =0.825, m m
iI
AX
zI
=0.025 ¸
=0.125 µ
=0.155, m =0.075, m
=0.200, m ´ =0.050, m ´
·I µ ´I µ ¶I ¶I
=0.200 µ
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13
m i =0.825, m
AS
=0.025 µ
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1
m z =0.825, m
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No.
From Table 15, it can be observed that the weight of each attribute is set to be bigger one by one in the first eight experiments. Weights of these eight attributes are
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set to be equal in the ninth experiment, which is m
zI µ
=0.125. In the tenth
experiment, attributes C1–C5 share a weight of 0.775 equally and attributes C6–C8
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share a weight of 0.225 equally. Contrary to the tenth experiment, the first three attributes share a weight of 0.225 equally and the last five attributes share a weight of
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0.775 equally in the eleventh experiment. In the twelfth experiment, attributes C1–C4
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share a weight of 0.800 equally and the rest four attributes C5–C8 share a weight of 0.200 equally. Contrary to the twelfth experiment, the first four attributes share a weight of 0.200 equally, while the last four attributes share a weight of 0.800 equally in the thirteenth experiment. Meanwhile, Fig. 5 illustrates the outcome of sensitivity analysis. Note that the comprehensive perception value . A
can be found in Table
15.
28
Fig. 5. Results of sensitivity analysis for thirteen experiments
It can be found from Table 15 and Fig. 5 that, among 10 out of 13 experiments, scheme A1 has the highest comprehensive perception value. Thus, the proposed
I2LI-RT method is relatively robust to the criteria weights m
!
with A1. In other
words, the proposed scheme evaluation method of DFD is feasible and robust. Besides, the ultimate rank of those schemes would change greatly with respective to different criteria weights, which suggested the importance of selecting qualified experts for sustainable performance evaluation of schemes for DFD.
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4.5.Discussions
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In this section, we discuss the experimental results from two aspects, i.e., 1) criteria analysis and improvement measures and 2) advantages of the proposed
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I2LI-RT method.
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a. Criteria analysis and improvement measures
As can be seen in Section 4.2, the weights of these eight criteria are obtained by
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using the proposed I2LI-RT method and those weights are plotted in Fig. 6 where
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some implication can be derived.
Fig. 6. Plot of the calculated criterion weights
(1) Disassembly accessibility (C2), fastener ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on evaluation of DFD refrigerator schemes based on sustainability since these factors carry the larger weights and are also above the average weight 0.1250, while production and use noise (C7) has the smallest weight among the eight criteria; 29
(2) Disassembly accessibility (C2) that refers to how difficult it is for disassembly tools to approach the parts of refrigerators has a largest impact on evaluation of DFD schemes based on sustainability. Generally speaking, a good disassembly accessibility can lead to the reduction of number and category of disassembly tools and the improvement of processing efficiency, which is related to structural design and layout. A deeper position of parts to be disassembled will bring greater difficulty to disassembly operations, thus in refrigerator product design, the location of parts with high recycling values should be set where they are easily available. Besides, designers should leave a larger space for compressor
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installation and simplify the installation method to facilitate installation and
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disassembly. Fastener ratio (C3) represents the proportion of the amount of connections in all elements and a smaller fastener ratio can make a better
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disassembly efficiency and promote the process of product recovery (Kondo et al.,
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2003). Typical fasteners include bolts, studs, screws, nuts, washers, pins and so on. However, excessive utilization of fasteners will cause loose fit between
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components when the connection condition is not qualified. Waste emissions (C8) can be divided into waste solids, waste liquids and waste gases, which can pose
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potential threats to human health and the global ecosystem (Lee et al., 2001; Tian
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et al., 2018a). Waste gases come from the organic waste gas emission during curing and waste liquids originate from the discharge of phosphating solution
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during phosphating treatment. Phosphate-rich solution is a nutrient-rich substance and discharging it without any chemical treatment will cause damage to the ecological environment, which does not satisfy the purpose of sustainable development. Disassembly energy consumption (C1) comes from various aspects and is mainly used to destroy the connection between components. Reasonable spatial layout and appropriate connection type can gain a lower disassembly energy consumption. For example, integrated connection type in which the coupling is integrated on the components can be adopted in refrigerator design. Production and use noise (C7) refers to the noise generated during the production and use of the refrigerator. Strong noise will cause hearing fatigue and even deafness for workers and users. Production noise comes from the installation of metal parts during the assembly process, as well as the process of punching and drilling during the assembly process. Use noise mainly comes from the start-up and operation of the compressor during use and the vibration of the pipeline in the 30
refrigerator during operation. And some improvement measures can be used to reduce those noise. For example, change the connection structure (reduce screws and riveting), reduce the portion of metal parts, use high-efficiency silent compressor, determine the optimal speed of the fan motor through the analysis of the pressure wave characteristics, optimize piping design and so on. As for toxic material proportion (C4), CFCs (chloro-fluoro-carbons) take a large part. Under normal conditions, CFCs are chemically stable and will evaporate at pretty low temperatures, thus they are ideal refrigerants for refrigerators and freezers. But CFCs will consume plenty of ozone in the ozone layer, which will destroy the
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ecological environment. At present, researches on CFCs alternative technology
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have made great progress and fluorine-free refrigerators have become mainstream products. The refrigerant has replaced R12 with R134a, and the blowing agent
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R11 has been replaced by cyclopentane (Liu 2004). Disassembly expense (C6)
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contains many aspects, such as labor costs, electricity costs and so on. Complex product designs will increase the expense of disassembly which will also lead to
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higher recovery costs. Reasonable structural design and appropriate material selection can reduce both energy disassembly consumption and disassembly
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expense. Material recovery rate (C5) depends on the structure of the refrigerator,
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the type of materials and compatibility among materials. Therefore, designers need to make a reasonable combination of parts (reduce the number of parts and
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the types of materials), choose compressors with less or no copper as much as possible, replace easy-to-soften PVC with other materials, and reduce the utilization of stainless steel products. b. Advantages
of the proposed I2LI-RT method
In the proposed I2LI-RT method, to better describe the fuzziness of human thinking, evaluate information is represented by I2LIFNs and the final optimal scheme is determined by RT. The adoption of I2LIFNs for representing and processing fuzzy information makes I2LI-RT easily capture the uncertainty of information and avoid information loss/distortion, and the introduction of RT assist I2LI-RT in objectively describing the emotions of decision makers by several pair comparisons, which are verified in Section 4.3. The sensitivity analysis in Section 4.4 demonstrates the robustness of the proposed method. In summary, the I2LI-RT method is effective and feasible to evaluate the sustainable performance of schemes of DFD. 31
5. Conclusion DFD is an effect product design technique from a disassembly point of review. A well-organized scheme of DFD should focus on both disassembly characteristics and environmental characteristics to achieve the goal of sustainable development. In this work, a hybrid MADM method, called I2LI-RT for short, was proposed to evaluate schemes of DFD based on sustainability under fuzzy environment. In the method, to better describe the fuzziness and ambiguity and avoid information loss/distortion in information aggregation phases, the concepts of I2LIFSs and I2LIFNs were firstly
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developed to represent the fuzzy evaluation information given by experts. In addition, an entropy weighting technology was utilized to determine the weights of different
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criteria and finally, RT was employed to order the alternatives and determine the
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optimal one.
As a case study has been applied, four refrigerator design schemes were selected
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as alternatives and an eight-criterion evaluation system of schemes of DFD for sustainability based on disassembly and environmental characteristics was established.
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Experimental results demonstrated that alternative AS was the optimal scheme based
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on fuzzy evaluation information, and disassembly accessibility (C2), fastener ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large
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impact on refrigerator’s sustainable design. Analysis of those criteria were conducted
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and the corresponding improvement measures of each criterion based on sustainability were also introduced. In addition, the comparative studies of I2LI-RT method with other four state of art methods indicated the feasibility and effectiveness of the proposed method and sensitivity analysis results verified its robustness and reliability. In summary, the proposed hybrid MADM method can be utilized to guide decision makers/manufacturers in making better decisions when choosing the most sustainable scheme of DFD. There are many future directions to provide new contributions for further research on the designation of a sustainable DFD scheme. First, encoding the hybrid MADM method and implanting the codes to computer programs for assessing schemes intelligently, can be suggested. Furthermore, employing the method to other application areas, such as environmental risk assessment, airlines safety evaluation and so on, is another challenging application for our paper. Due to the uncertainty and fuzziness of evaluation information, other uncertain theories can be integrated into the 32
proposed method (Zhang et al., 2020). At last but not least, integrating the proposed hybrid method with recent advances in the evolutionary computation is another interesting addition for future studies (Fathollahi-Fard et al., 2020).
Acknowledgement This work is supported in part by National Natural Science Foundation of China
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under Grant No. 51775238, Science and Technology Development Project of Jilin
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Province under Grant Nos 20180101060JC and 20180101058JC.
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Interest statement statement
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We claim no conflict of interest