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Resources, Conservation and Recycling 103 (2015) 125–138

Contents lists available at ScienceDirect

Resources, Conservation and Recycling

journa l homepage: www.e lsev ier .com/ locate / resconrec

reen decision-making model in reverse logistics using FUZZY-VIKORethod

li Haji Vahabzadeh a, Arash Asiaei b, Suhaiza Zailani c,∗

Department of Information Systems and Operations Management, The University of Auckland Business School, Auckland, 1010, New ZealandAdvanced Informatics School, Universiti Teknologi Malaysia, International Campus, Jalan Semarak, 54100 Kuala Lumpur, MalaysiaFaculty of Business and Accountancy, University of Malaya, 50603, Lembah Pantai, Kuala Lumpur, Malaysia

r t i c l e i n f o

rticle history:eceived 27 December 2013eceived in revised form 31 March 2015ccepted 5 May 2015

eywords:everse logistics (RL)reenUZZY-VIKORecision-making model

a b s t r a c t

Due to the increasing global environmental consciousness and sustainability concerns, different indus-tries that deal with Reverse Logistics (RL) are seeking methods to measure and analyze the impacts of theirRL activities on the environment. However, making the greenest decision in the vague and complex areaof RL makes this process somewhat difficult. Hence, to address these issues and provide a more metic-ulous and closer approach to the real world situations, a FUZZY-VIKOR method using interval-valuedtrapezoidal fuzzy numbers is proposed in the current research. As the further discussions explain, first,the significant factors in environmental sound practices together with the main processes and recoveryoptions in RL are identified. Second, the influences of each green environmental factor on each RL recov-ery option are analyzed and ranked. To obtain concise results, the elicitation of experts is sought fromamong academicians and industry. The final results illustrate that, intriguingly, disposing of the returnshas the lowest negative impact on the environment; thereby the best recovery option, while reselling ofthe returns was perceived as the worst recovery option. This research also suggests new directions forfuture research. From the managerial point of view, it would be interesting to study a sustainable reverselogistics through the proposed model. We only considered the impacts of environmental factors on RL,while the final decision will be more exact if the economic and societal aspects of RL are also analyzed.In addition, to reflect the technical views of all the stakeholders in RL towards the best recovery optionand also take into account their concerns, we suggest designing a group decision making model acrossthe RL using the Fuzzy-MADM methods.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

In recent years, the increasing awareness of environmental dilemmas in reverse logistics (RL) has attracted the attention of manufac-urers and encouraged them to redesign their RL processes and networks according to green concepts. A number of efforts are being madeo minimize the destructive effects of RL on the environment. In this respect, the environmental considerations, legal regulations, andhe related economic advantages have also prompted several companies, such as General Motors, Kodak and Xerox, to consider RL andssociated recovery processes (Meade et al., 2007; Üster et al., 2007). Since the main discussions about RL and its environmental mattersere initiated by the works carried out by Rogers and Tibben-Lembek over the last decade, companies with RL processes have embarked

n taking “green” and sustainability into account. In order to reduce the impacts of pollution on the environment, reverse logistics haveeen analyzed (Byrne and Deeb, 1993; Carte and Ellram, 1998; Wu and Dunn, 1995).

In this context, the Malaysian government has launched several progressive policies to support its national agenda on reverse logistics

ctivities. For example, the Tenth Malaysia Plan (2011–2015) put forward by the government is based on the fundamental issue of sustain-ble production activities that could balance economic growth and environmental degradation. Moreover, many companies announced inheir websites that they have reverse logistics programs. HP declared that it has two basic programs for reverse logistics; HP trade-in andP buy-back. The HP Trade-In program offers HP customers cash payments for their old equipment when new HP products are purchased.

∗ Corresponding author.E-mail addresses: a.vahabzadeh@auckland.ac.nz (A. Haji Vahabzadeh), aarash5@live.utm.my (A. Asiaei), shmz@um.edu.my (S. Zailani).

ttp://dx.doi.org/10.1016/j.resconrec.2015.05.023921-3449/© 2015 Elsevier B.V. All rights reserved.

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26 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

n HP buy-back, HP collects, tests and evaluates the equipment. If the equipment has market value it will be refurbished, resold to theecondhand market. If the equipment has no value, it will be disposed of in accordance to HP’s strict global recycling standards (HP, 2007).okia designed a program for product take-back that aims at collecting products at the end of its service life with a view to recovering itsaterial and energy content as well as ensuring safe treatment of substances that may cause harm to people or the environment (Nokia,

002). Dell apply industry leading recycling program that enable customers to recycle or donate their PCs for free (Dell, 2007).With respect to environmental matters, the role of reverse logistics and the associated influences on developing the concept of

ustainability and environmental protection have been explained (Brito et al., 2003; Fernández, 2004; Krikke et al., 1998). Rogers andibben-Lembek (1998) discussed the negative impacts of recovery options on the environment, such as disposing, landfilling, and inciner-tion of returns. In order to improve the recovery process within RL, an environmental study considering the life cycle analysis in the batteryector was carried out (Tsoulfas et al., 2002). The increase in CO2 emissions and greenhouse gases (GHG) due to unnecessary processes inL, such as extra transportation, would be minimized if the green and RL processes could be integrated in a holistic and unique approach.

In addition, legislative policies with respect to environmental regulations and sustainability have enforced manufacturers to accept theesponsibility of taking back their returns. Nonetheless, many companies are not capable of applying the current techniques and modelso satisfy these requirements. One of the main obstacles in this regard is to measure the environmental contribution of certain activities inL; especially, when the impacts of a group of environmental factors should be ranged and interpreted for a group of RL recovery options.herefore, the need for a comprehensive technique that is able to cope with all these issues appears necessary.

In order to solve the ambiguous part of this problem, which is interpreting the impacts of environmental elements on RL recoveryptions, first, the linguistic terms and weights are defined in a reasonable range. This possibility facilitates the process of impact analysisor the experts during the interview sessions. Second, the equalization of qualitative terms into quantitative values by using interval-alued trapezoidal fuzzy numbers is performed. Ultimately, the FUZZY-VIKOR is applied to acquire the final ranking. The rest of thisrticle is organized as follows: The following section briefly reviews the background literature. The third section describes the researchethodology for testing the method of VIKOR, and the fifth section discusses the results of the data analyses. The article concludes with a

elineation of the significance of the findings, managerial implications, and future research directions.

. Literature review

.1. Reverse logistics (RL) vs. green logistics (GL)

Rogers and Tibben-Lembek (1998) defined RL as: “the process of planning, implementing, and controlling the efficient, cost effectiveow of raw materials, in-process inventory, finished goods and related information from the point of consumption to the point of origin

or the purpose of recapturing value or proper disposal”. According to the definition of Dowlatshahi (2000), RL is “a process in which aanufacturer systematically accepts previously shipped products or parts from the point for consumption for possible recycling, reman-

facturing or disposal”. He considered the strategic and operational factors for implementing efficient reverse logistics in the company.ased on his approach, in the process of implementing holistic reverse logistics, the strategic factors, such as cost, quality, customer service,nvironmental effects, and regulations, are more critical than the operational factors like cost benefit analysis, transportation, warehousing,upply management, remanufacturing, recycling, and packaging.

On the other hand, Fleischmann et al. (2001) described RL as: “a process of planning, implementing and controlling the efficient, effectivenbound flow and storage of secondary goods and related information opposite to the traditional supply chain directions for the purposef recovering value and proper disposal”. Reverse logistics requires supply chain members to coordinate and integrate environmentalanagement with the traditional logistics functions of transportation, packaging, labeling and warehousing. Pohlen and Theodore Farris

1992) find that the requirements for reverse logistics vary noticeably across firms and have important environmental and economic impli-ations. The environmental aspects focus on resource reduction, materials substitutions and waste reduction, whereby companies becomeore environmentally efficient and help finding solutions for environmental problems. The economic aspects emphasize recapturing value

rom the returned products, such as retrieving integrated circuit boards from electronic products, or recovering valuable materials fromhe product through the recycling process.

While, “Green Logistics (GL) is a form of logistics which is calculated to be environmentally and often socially friendly in addition toconomically functional (Smith, 2012)”. The MGC Institute of Logistics in Vietnam (2010) described green logistics as “The managementf the logistics and supply chain process including the incorporation of environmentally sustainable strategies that assist in minimizinghe effects of pollution, particulate emissions and the management of processes to overcome climate change”. Carter and Rogers (2008)tated that “Green logistics consists of all activities related to the eco-efficient management of the forward and reverse flows of productsnd information between the point of origin and the point of consumption whose purpose is to meet or exceed customer demand”. Rogersnd Tibben-Lembek (1998) considered that “Green logistics, or ecological logistics, refers to understanding and minimizing the ecologicalmpact of logistics. Green logistics activities include measuring the environmental impact of particular modes of transport, ISO 14000ertification, reducing energy usage of logistics activities, and reducing usage of materials”.

Both definitions as above, however, have led some authors to suggest that reverse logistics is imperative to the green logistics (Autryt al., 2001; Knemeyer et al., 2002), green marketing (Wu and Dunn, 1995; Carter and Rogers, 2008) and sustainability (Markley and Davis,007; Carter and Easton, 2011). By transforming the returns into products with value in the market, reverse logistics allow the supply chaino be in circulation so that the waste can be minimized through the process (Andic et al., 2012). Hence, the best approach by companies tochieve the environmental protection is by introducing the reverse flow of supply chain that can maximize the value of the product returnsKumar and Malegeant, 2006). The reverse logistics therefore, have been widely recognized in the literature as the major component thatreates value for managing the product recovery, product returns or excessive stock in the market (Jayant et al., 2012). Reverse logistics

lso has become a main part of green logistics due to its contribution in reducing the waste generated through several recovery activitiesuch as reuse, remanufacturing and recycling (Hervani et al., 2005).

Nevertheless, besides the benefits that firms may enjoy by implementing effective reverse logistics, many business organizations stillgnored and not proactive in carrying out the reverse logistics activities (González-Torre et al., 2010). This is because many of them believe

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A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138 127

hat the impediments are much greater than the benefits they will obtain in adopting the reverse logistics activities (Tibben-Lembke, 2002)nd prefer to rely on the traditional way of doing business by concentrating on the forward logistics to achieve the competitive advantageFine et al., 2002). In this circumstance, the focus of building the green value chain by business organization lies in the scope of forwardather than reverse logistics. Nevertheless, such conventional approach appeared to be incomplete due to the imbalance focus in creatingalue of returns products.

.2. Reverse logistics and recapturing the value of returns

Most of the manufacturer’s targets are just to deliver their products to their customers, while by ignoring the efficient return and refur-ishment or disposal of the product, many companies miss out on a significant return on investment. Logisticians who treat reverse logisticss a way to maximize the value of returned assets make a significant contribution to their company’s bottom line (Andel, 1997; Clendenin,997; South, 1998). By improving customer satisfaction, leveraging resource investment, and reducing warehouse and transportation costshe effective reverse logistics will be achieved to direct benefits (Guintini and Andel, 1994; Andel, 1997). Reverse logistics also affects onustomer satisfaction by accelerating the process of returns handling when any critical repair or remanufacturing is needed (Blumberg,001). Companies with the ability of making the value of the returns may stay longer in the business. If a company implements the reverse

ogistics system, it will gain money (Stock, 1998). Recapturing the value of the returns through refurbishment, remanufacturing, repair,nd recycling can bring various profits for the company in the competitive markets (Giuntini and Andel, 1995).

.3. Multi criteria decision-making models and reverse logistics

“MCDM can be defined as the study of methods and procedures by which concerns about multiple conflicting criteria can be formallyncorporated into the management planning process” (International Society on Multiple Criteria Decision Making). MCDM also referss Multi-Criteria Decision Analysis (MCDA) or Multiple Criteria Analysis (MCA); Multi-Dimensions Decision Making (MDDM), and Multittributes Decision Making (MADM). The aim of MCDM is to give solutions and proposes the best or a set of good alternative (s) for solving

he problems with multiple criteria. The results will be affected by decision makers’ priorities during giving ranks to the criteria andubcriteria. These methods can be applied in both quantitative and qualitative criteria by sharing the common characteristics of opposemong criteria, incommensurable units, and hard in design/selection of alternatives (Pohekar and Ramachandran, 2004).

According to the reviewed literature, MCDM methods have been widely employed in various domains of reverse logistics, includingvaluating and selection the Third-Party Reverse Logistics Providers (3PRLPs), modeling product recovery, waste management, assessmentf different alternatives for End-of-Life (EOL). Table 1 shows some application of the MCDM methods in the RL literature.

Unlike the majority of the researches on supplier evaluation and selection in RL in which the FAHP model has been opted, in a recenttudy which has been done by Amin and Zhang (2012), a method based on linguistic variables and triangular fuzzy numbers (TFNs) haseen proposed for the supplier evaluations. According to the authors, the new model would take lesser time than FAHP method and it isore appropriate when there are a large number of assessment criteria.

.4. Fuzzy sets and theory

Fuzzy logic has been proposed (Zadeh, 1965, 1996, 1997) as an analytical approach to integrate uncertainty into decision-making models.ncomplete information also has this possibility to take into account in all necessary calculation in Fuzzy logic despite the behind reasons.n fact, fuzzy logic provides a suitable and applicable basis for considering the vague reasoning instead of the exact one. By employing fuzzyools many advantages deliver to the users. Fuzzy tools provide a new methodology which is more simple and it can reduce the analysisnd development time of the model. Consequently, the implementation and adoption of fuzzy tools are uncomplicated. Fuzzy tools haveresented a higher level of performance than other soft methods in decision making problems under uncertainty. Nonetheless, they have

user-friendly platform (Azadegan et al., 2011).A rapid growth has been seen in using fuzzy logic to different fields of manufacturing during the past two decades. Fuzzy logic considers

he variables according to their degree of membership, rather than absolute membership at its most basic form. A level of tolerance foragueness consider by fuzzy logic, instead of exactness and precision. All imperfect information, which could be the result of impreciseeasurements or obtained through inaccurately codifying expert elicitation, is able to take into consideration in a fuzzy modeling. Indeed,

he attempts of fuzzy logic are to imitate the human brain to apply the methods of reasoning effectively which are imprecise instead ofigorous. Fuzzy logic provides the recognition of indefinite dependencies among models, by considering the involvement of inexactituden membership. Crisp logic is a totally different approach, which reasoning and assessments are binary and based on propositional logic.ariables take a range between 0 and 1 in fuzzy logic and they are not essentially limited to that binary restriction. In this regard, a variableas a degree of membership in a fuzzy set (Azadegan et al., 2011).

A fuzzy set has been defined as a class of objects which have a continuum of membership grades and is typically shown by putting ailde ‘∼’ above the specified symbol in this matter (Kahraman et al., 2004). Chen (1985) and Chen and Hsieh (1999) specified generalizedrapezoidal fuzzy numbers and their related operations. In Fig. 1 General trapezoidal fuzzy numbers (Chen and Chen,2003b) are presented

˜ = (a1, a2, a3, a4; wA) and B = (b1, b2, b3, b4; wB) representing two different decision-makers ideas, which 0 < wA ≤ 1 and 0 < wB ≤ 1;

A and wB indicate the level of assurance regarding the decision-maker’s ideas A and B, respectively (Chen and Chen, 2003a,b, 2007).

.5. VlseKriterijumska optimizacija I kompromisno resenje (VIKOR) method

“The VIKOR method was proposed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuminghat compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and thelternatives are evaluated according to all established criteria” (Opricovic et al., 2007). Opricovic (1998) developed the initial VIKORethod. The VIKOR method is the optimization and compromise solution in MCDM, which is appropriate for estimating each alternative

128 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

Table 1MCDM methods in reverse logistics.

Year Author Objective Method

2007 Zhang and Feng Selection process of reverse logistics provider FAHPStaikos and Rahimifard Product recovery of shoes AHP

2008 Pati et al. Manage the paper recycling in logistics systems Mixed integer goal programming (MIGP)Efendigil et al. Select the best 3PRLPs FAHP and ANNFernandez and Kekale A conceptual decision-making model under

multiple conflicting criteria: the case of reverselogistics

AHP and Delphi

2009 Kannan Selection of 3PRLPs AHP and FAHPKannan et al. The selection of 3PRLPs Interpretive structural modeling (ISM) and

fuzzy TOPSISWadhwa et al. Designing effective and efficient flexible return

policyFAHP

2010 Hernandez et al. Analyzed the effect of reverse logistics practiceon automotive corporate performance

AHP and ANP

Geethan et al. Selection of collecting center location in thereverse logistics network

AHP and TOPSIS

2011 Govindan and Murugesan Select the 3PRLPs Fuzzy extent analysisSasikumar and Haq Selection of the best 3PRLP FMCDM and VIKORAzadi and Saen Selecting 3PRLPs New chance-constrained data envelopment

analysis (CCDEA)Jiang et al. Selecting remanufacturing technology AHPBarker and Zabinsky Designing the reverse logistics network AHP

2012 Divahar and Sudhahar Selecting and evaluating of RL providers AHPGovindan et al. Selection of 3RPRLP ISMSenthil et al. Selection and evaluation of RL channels Fuzzy AHP-TOPSISHsu et al. Select the vendors for the recycled material DEMATEL-ANP (DANP)Amin and Zhang Supplier evaluations in RL Linguistic variables and triangular fuzzy

numbers (TFNs)Chiou et al. Analyze the important criteria and sub-criteria

in RL implementationFAHP

Akdogan and Cos kun Surveyed the drivers involved in RL activitiesin the house appliance industry in Turkey andranked them

AHP

2013 Govindan et al., 2013 Select a third-party reverse logistic provider ANPJindal and Sangwan Evaluation of sustainable reverse logistics

network modelsFuzzy AHP-TOPSIS

Shaik and Abdul-Kader, 2013a; Shaik andAbdul-Kader, 2013b

A comprehensive performance measurementmethodology for transportation in reverselogistics

AHP

2014 Shaik and Abdul-Kader, 2014 Comprehensive performance measurementand causal-effect decision making model forreverse logistics enterprise

DEMATEL

Senthil et al. Contractor evaluation and selection inthird-party reverse logistics

AHP-Fuzzy TOPSIS

Tajik et al., 2014 Sustainable third-party reverse logisticsprovider selection

Fuzzy AHP-TOPSIS

fiPVnV

Mfsm

Fig. 1. General trapezoidal fuzzy numbers∼A and

∼B.

or each criterion (Opricovic, 1998; Opricovic and Tzeng, 2002, 2004; Opricovic et al., 2007; Huang et al., 2009). This method can be appliedn the complex multi-criteria system (Opricovic and Tzeng, 2004). The extended VIKOR method was developed and compared with TOPSIS,ROMETHEE, and ELECTRE (Opricovic et al., 2007). A comparative analysis for identifying the differences and similarities between theIKOR and TOPSIS methods was performed (Opricovic and Tzeng, 2004). The results showed that these two methods employ variousormalizations with different aggregating functions for ranking. In another comparison, the extended VIKOR method was compared withIKOR, TOPSIS, ELECTRE, and PROMETHEE on the basis of resolving the algorithm (Opricovic et al., 2007).

Chatterjee et al. (2009) compared two methods – VIKOR and ELECTRE – for material selection. Tsai et al. (2011) proposed a combined

ADM model by integrating ANP and the VIKOR method, which is applicable for governments to evaluate their policies and the efforts

or improving their policies, effectively. Mohaghar et al. (2012) used FAHP and the VIKOR method in selecting marketing strategy. In thistudy, the VIKOR method was used to rank the strategies with regard to sub criteria. Chang and Hsu (2011) applied the modified VIKORethod and proposed a modified VIKOR index Qj* for identifying the environmental factors and the level of vulnerability that can affect

A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138 129

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Fig. 2. Sustainable distribution: a strategy.ource: sustainable distribution: a strategy (DETR, 1999)

he land use within the watershed. Fazli and Jafari (2012) developed a hybrid multi-criteria model for the stock market and the VIKORlgorithm was applied to rank and choose the best investment alternatives.

Sasikumar and Haq (2011) used the VIKOR method in a fuzzy multi-criteria decision-making (FMCDM) model for the selection of bestPRLP. Sanayei et al. (2010) employed the VIKOR method for the supplier selection under the fuzzy environment. In the field of supplierelection, a fuzzy VIKOR method based on the entropy measure for objective weighting has been discussed (Shemshadi et al., 2011).alahzaghard et al. (2011) used Fuzzy Delphi, FAHP, and SIR.VIOKOR for supplier selection. Combining VIKOR, GRA and interval valued

uzzy sets has been studied to estimate the service quality of Chinese cross-strait passenger airline via customer survey, and to identifyhe gaps, weaknesses and strengths in the quality of the services (Kuo, 2011).

. Methodology

The methodological approach in the current research is divided into three main steps. In the first step, the concept of the generalizedrapezoidal fuzzy numbers is explained. In the second step, the working steps in the VIKOR method are described. In the final step, in ordero obtain the appropriate results and verify the proposed model, expert interviews are performed. In this part, the environmental factorsre adopted from the “Sustainable Distribution: A Strategy” (DETR, 1999), as shown in Fig. 2, and the six recovery options are chosen fromogers and Tibben-Lembek (1998).

.1. The conception of generalized trapezoidal fuzzy numbers

Definition (Chen, 1985): The definition of a generalized trapezoidal fuzzy number is presented as a vector A = (a1, a2, a3, a4; wA), andlso the membership function a(x) : R → [0, 1] can be illustrated as follows:

a(x) =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

x − a1

a2 − a1× wA,

wA,

x − a4

a3 − a4× wA,

0,

x ∈ (a1, a2)

x ∈ (a2, a3)

x ∈ (a3, a4)

x ∈ (−∞, a1)U(a4, ∞)

(1)

here a1 ≤ a2 ≤ a3 ≤ a4 and wA ∈ [0, 1]

The generalized trapezoidal fuzzy numbers elements x∈R are real numbers, and its membership function a(x) is defined as the frequent

nd continuous convex function, which demonstrates the membership degree of the fuzzy sets. If −1 ≤ a1 ≤ a2 ≤ a3 ≤ a4 ≤ 1, then A isecognized as the normalized trapezoidal fuzzy number. Particularly, if wA = 1, then A can be called trapezoidal fuzzy number (a1, a2, a3, a4);f a1 < a2 = a3 < a4, then A is decreased to a triangular fuzzy number. If a1 = a2 = a3 = a4, then A is decreased to a real number.

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30 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

.1.1. The generalized trapezoidal fuzzy numbers operation rulesAssume that a = (a1, a2, a3, a4; wa) and b = (b1, b2, b3, b4; wb) are two generalized trapezoidal fuzzy numbers, then the operational

ules of the generalized trapezoidal fuzzy numbers a and b are demonstrated as follows (Chen and Chen, 2009):

a ⊕ b = (a1, a2, a3, a4; wa) ⊕ (b1, b2, b3, b4; wb)

= (a1 + b1, a2 + b2, a3 + b3, a4 + b4; min(wa, wb))(2)

a − b = (a1, a2, a3, a4; wa) − (b1, b2, b3, b4; wb)

= (a1 − b4, a2 − b3, a3 − b2, a4 + b1; min(wa, wb))(3)

a⊗ b = (a1, a2, a3, a4; wa) ⊗ (b1, b2, b3, b4; wb) = (a, b, c, d; min(wa, wb)) (4)

here,

a = min(a1 × b1, a1 × b4, a4 × b1, a4 × b4) ,

b = min(a2 × b2, a2 × b3, a3 × b2, a3 × b3) ,

c = max(a2 × b2, a2 × b3, a3 × b2, a3 × b3) and,

d = max(a1 × b1, a1 × b4, a4 × b1, a4 × b4)

f a1, a2, a3, a4, b1, b2, b3, b4 are real numbers, then:

a ⊗ b = (a1 × b1, a2 × b2, a3 × b3, a4 × b4; min(wa, wb))

a

b= (a1, a2, a3, a4; wa)

(b1, b2, b3, b4; wb)= (a1

b4,a2

b3,a3

b2,a4

b1; min(wa, wb)) (5)

.1.2. The center of gravity (COG) point of generalized trapezoidal fuzzy numbersThe concept of COG point of generalized trapezoidal fuzzy numbers was presented by Chen and Chen, 2003a; it assumes that the COG

oint of the generalized trapezoidal fuzzy number a = (a1, a2, a3, a4; wa) is (xa, ya), then:⎧⎪⎪⎪⎨⎪⎪⎪⎩ya =

⎧⎨⎩

wa ×(a3 − a2

a4 − a1+ 2

)6

wa⁄2ifa1 = a4

ifa1 /= a4

⎫⎬⎭

xa = ya × (a2 + a3) + (a1 + a4) × (wa − ya)2 × wa

⎫⎪⎪⎪⎬⎪⎪⎪⎭

(6)

.1.3. Interval-valued trapezoidal fuzzy numbers (Wei and Chen, 2009)Wang and Li (2001) proposed the interval-valued trapezoidal fuzzy numbers

˜A =[

˜AL, ˜AU]

= [(aL1, al2, aL3, aL4; w ˜AL), (aU1 , aU2 , aU3 , aU4 ; w ˜A

U)]

here 0 ≤ aL1 ≤ aL2 ≤ aL3 ≤ aL4 ≤ 1, 0 ≤ aU1 , ≤ aU2 ≤ aU3 ≤ aU4 ≤ 1, 0 ≤ w ˜AL ≤ w ˜A

U ≤ 1 and ˜AL

⊂ ˜AU

.

.1.4. The operation rules of interval-valued trapezoidal fuzzy numbers (Wei and Chen, 2009)Assume that:

˜A =[

˜AL, ˜AU]

= [(aL1, al2, aL3, aL4; w ˜AL), (aU1 , aU2 , aU3 , aU4 ; w ˜A

U)]

nd:

˜B =[

˜BL, ˜BU]

= [(bL1, bl2, bL3, bL4; w ˜BL), (bU1 , bU2 , bU3 , bU4 ; w ˜BU)]

re the two interval-valued trapezoidal fuzzy numbers, where:0 ≤ aL1 ≤ aL2 ≤ aL3 ≤ aL4 ≤ 1, 0 ≤ aU1 , ≤ aU2 ≤ aU3 ≤ aU4 ≤ 1, 0 ≤ w ˜AL ≤ w ˜A

U ≤ 1

nd ˜AL

⊂ ˜AU

, 0 ≤ bL1 ≤ bL2 ≤ bL3 ≤ bL4 ≤ 1, 0 ≤ bU1 , ≤ bU2 ≤ bU3 ≤ bU4 ≤ 1, 0 ≤ w ˜BL ≤ w ˜B

U ≤ 1 and w ˜BL ⊂ w ˜B

U.The operations are presented as follows:

The sum of two interval-valued trapezoidal fuzzy numbers ˜A⊕ ˜B:

˜A ⊕ ˜BL l L L U U U U L l L L U U U U

= [(a1, a2, a3a4; w ˜A

L), (a1 , a2 , a3 a4 ; w ˜AU)] ⊕ [(b1, b2, b3, b4; w ˜B

L)], (b1 , b2 , b3 , b4 ; w ˜BU)

= [(bL1 + bL1, bl2 + bl2, al3 + bl3, aL4 + bL4; min(w ˜AL, w ˜B

L)), (aU1 + bU1 , aU2 + bU2 , aU3 + bU3 , aU4

+bU4 ; min(w ˜AU, w ˜B

U))]

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A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138 131

The difference of two interval-valued trapezoidal fuzzy numbers ˜A− ˜B:

˜A− ˜B =[(aL1, al2, aL3a

L4; w ˜A

L), (aU1 , aU2 , aU3 aU4 ; w ˜A

U)] − [(bL1, bl2, bL3, bL4; w ˜BL)], (bU1 , bU2 , bU3 , bU4 ; w ˜B

U)

= [(aL1 − bL4, al2 − bl3, al3 − bl2, aL4 − bL1; min(w ˜AL, w ˜B

L)), (aU1 − bU4 , aU2 − bU3 , aU3

−bU2 , aU4 − bU1 ; min(w ˜AU, w ˜B

U))]

(8)

The product of two interval-valued trapezoidal fuzzy numbers ˜A⊗ ˜B:

˜A ⊗ ˜B =[(aL1, al2, aL3a

L4; w ˜A

L), (aU1 , aU2 , aU3 aU4 ; w ˜A

U)] ⊗ [(bL1, bl2, bL3, bL4; w ˜BL)], (bU1 , bU2 , bU3 , bU4 ; w ˜B

U)

= [(aL1 × bL1, al2 × bl2, aL3 × bL3, aL4 × bL4; min(w ˜AL, w ˜B

L)), (aU1 × bU1 , aU2 × bU2 , aU3 × bU3 , aU4

×bU4 ; min(w ˜AU, w ˜B

U))]

(9)

The quotient of two interval-valued trapezoidal fuzzy numbers ˜A/ ˜B:

˜A/ ˜B = [(aL1, al2, aL3, aL4; w ˜AL), (aU1 , aU2 , aU3 a

U4 ; w ˜A

U)]/[(bL1, bl2, bL3, bL4; w ˜BL)], (bU1 , bU2 , bU3 , bU4 ; w ˜B

U)] =[(aL1bL4,aL2bl3,aL3bL2,aL4bL1

; min(w ˜AL, w ˜B

L)

),

(aU1bU4,aU2bU3,aU3bU2,aU4bU1

; min(w ˜AU, w ˜B

U)

)] (10)

The product between an interval-valued trapezoidal fuzzy number and a constant � ˜A:

� ˜A = � × [(aL1, al2, aL3, aL4; w ˜AL), (aU1 , aU2 , aU3 a

U4 ; w ˜A

U)]

= [(�aL1, �al2, �aL3, �aL4; w ˜AL)], (�aU1 , �aU2 , �aU3 , �aU4 ; w ˜A

U)], � > 0(11)

.1.5. The distance of interval-valued trapezoidal fuzzy numbersAssume that:

˜A = [ ˜AL, ˜AU

] = [(aL1, al2, aL3, aL4; w ˜AL), (aU1 , aU2 , aU3 a

U4 ; w ˜A

U)]

nd:

˜B = [ ˜BL, ˜BU

] = [(bL1, bl2, bL3, bL4; w ˜BL), (bU1 , bU2 , bU3 , bU4 ; w ˜B

U)]

re two generalized trapezoidal fuzzy numbers, then the distance of two interval-valued trapezoidal fuzzy numbers ( ˜Aand˜B) is computeds follows:

Use the formula (6) to calculate the coordinate of COG points (x ˜AL, y ˜A

L), (x ˜AU, y ˜A

U), (x ˜BL, y ˜B

L), (x ˜BU, y ˜B

U), which belong to the generalized

trapezoidal fuzzy numbers ˜AL, ˜AU, ˜BL, ˜BU

, respectively. The distance of two interval-valued trapezoidal fuzzy numbers is:

d(

˜A, ˜B)

=√((y ˜A

L − y ˜BL)2 + ((x ˜A

L − x ˜BL)2 + ((y ˜A

U − y ˜BU)2 + ((x ˜A

U − x ˜BU)2

⁄4(12)

here d( ˜A, ˜B) satisfies the following properties:

(i) If ˜A and ˜B are normalized interval-valued trapezoidal fuzzy numbers, then: 0 ≤ d(

˜A, ˜B)

≤ 1

(ii) ˜A = ˜B⇔ d(

˜A, ˜B)

= 0

iii) d(

˜A, ˜B)

= d(

˜B, ˜A)

iv) d(

˜A, ˜C)

+ d(

˜C, ˜B)

≥ d(

˜A, ˜B)

.2. The working steps in the VIKOR method

It can be difficult to obtain the type of generalized interval-valued trapezoidal fuzzy numbers for the attribute values and weights directlyy the decision makers in the real decision-making situation. Accordingly, the form of linguistic terms is usually adopted. Hence, Wei and

132 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

Table 2Interval linguistic terms and relative interval-valued trapezoidal fuzzy numbers.

Linguistic term(the attribute values) Linguistic terms (weights) Generalized interval-valued trapezoidal fuzzy numbers

Absolutely-poor (AP) Absolutely-Low (AL) [(0.00,0.00,0.00,0.00;0.8), (0.00,0.00,0.00,0.00;1.0)]Very-poor (VP) Very-low|(VL) [(0.00,0.00,0.02,0.07;0.8), (0.00,0.00,0.02,0.07;1.0)]Poor (P) Low (L) [(0.04,0.10,0.18,0.23;0.8), (0.04,0.10,0.18,0.23;1.0)]Medium-poor (MP) Medium-low (ML) [(0.17,0.22,0.36,0.42;0.8), (0.17,0.22,0.36,0.42;1.0)]Medium (F) Medium (M) [(0.32,0.41,0.58,0.65;0.8), (0.32,0.41,0.58,0.65;1.0)]Medium-good (MG) Medium-high (MH) [(0.58,0.63,0.80,0.86;0.8), (0.58,0.63,0.80,0.86;1.0)]

CT

cLaf

Ig

1

•

c

•

•

Good (G) High (H) [(0.72,0.78,0.92,0.97;0.8), (0.72,0.78,0.92,0.97;1.0)]Very-good (VG) Very-high (VH) [(0.93,0.98,1.00,1.00;0.8), (0.93,0.98,1.00,1.00;1.0)]Absolutely-good (AG) Absolutely-high (AH) [(1.00,1.00,1.00,1.00;0.8), (1.00,1.00,1.00,1.00;1.0)]

hen (2009) applied the interval-valued trapezoidal fuzzy numbers and its relative’s 9-member linguistic terms, which are presented inable 2

Assuming that each alternative is evaluated according to each attribute function, the compromise ranking could be performed byomparing the measure of closeness to the ideal alternative. The multi-attribute measure for compromise ranking is developed from theP – metric used as an aggregation function in a compromise programming method (Flerov, 1973; Zeleny, 1982). The various m alternativesre denoted as A1, A2, ..., Am. For alternative Ai, the rating of the jth aspect is denoted by fij , that is, fij is the value of jth attribute functionor the alternative Ai; n is the number of attribute. Development of the VIKOR method is started with the following form of LP – metric:

Lp,i =

⎧⎨⎩

n∑j=1

[wj(f ∗j − fij)⁄

(f ∗j

− f −j

)]p⎫⎬⎭

1⁄p

1 ≤ p ≤ ∞; i = 1, 2, ..., m

n the VIKOR method, L1,i (as Si) and L∞,i (as Ri) are used to formulate ranking measure. The solution obtained by miniSi is with a maximumroup utility (“majority” rule), and the solution obtained by miniRi is with a minimum individual regret of the “opponent”.

Establish the positive ideal solution and the negative ideal solution of the evaluation objects.

Assume that the positive ideal solution and the negative ideal solution are: ˜V+

= [˜v+j ]

1×n,˜V

−= [˜v

−j ]

1×n, then:

˜v+j = [(vL+

j1 , vL+j2 , vL+

j3 , vL+j4 ; wL+

j), (vU+

j1 , vU+j2 , vU+

j3 , vU+j4 ; wU+

j)]

=

⎡⎢⎣

(maxi

(vLij1), (max

i

(vLij2), (max

i

(vLij3), max

i

(vLij4); (max

i

(wLij

)),(maxi

(vUij1), (max

i

(vUij2)

), (max

i

(vUij3), max

i

(vUij4); (max

i

(wUij

))

˜v−j = [(vL−

j1 , vL−j2 , vL−

j3 , vL−j4 ; wL−

j), (vU−

j1 , vU−j2 , vU−

j3 , vU−j4 ; wU−

j)]

=

⎡⎢⎣

(mini

(vLij1), (min

i

(vLij2), (min

i

(vLij3), min

i

(vLij4); (min

i

(wLij

)),(mini

(vUij1), (min

i

(vUij2)

), (min

i

(vUij3), min

i

(vUij4); (min

i

(wUij

))

Compute the weighted matrix and the COG of every attribute with respect to the positive ideal solution and the negative ideal solution.

According to the formula (6), we can compute the COG [(y, x)v]6×5 of every element in the weighted matrix and the barycentricoordinates [(y, x)v+5 ]5 and [(y, x)v− ]5 of each element with respect to the positive ideal solution and the negative ideal solution.

Calculate the values Si and Ri, i = 1, 2, ..., m by the relations:

Si =n∑j=1

[d(˜v

+j , ˜vij)⁄d(˜v

+j , ˜v

−j )

]

Ri = maxj

[d(˜v

+j , ˜vij)⁄d(˜v

+j , ˜v

−j )

]

Calculate the values Q , i = 1, 2, ..., m by the following relation:

i

Qi = v(Si − S∗)(S− − S∗)

+ (1 − v)(Ri − R∗)(R− − R∗)

A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138 133

Table 3Weights for environmental factors according to the decision-makers.

Attribute Climate change(contributes to GHGreduction

Air quality (meetsinternational standard)

Noise (meetsinternational standard)

Land use andbiodiversity(minimizes the impactson biodiversity ofspecies habitats andlandscapes)

Waste management(minimizes waste andimpact of wastes)

Decision maker VH MH M VL AH

Table 4Impacts of reverse logistics’ decision option (alternative) on environmental factors.

Attribute Climate change(contributes to GHGreduction)

Air quality (meetsinternational standard)

Noise (meetsinternational standard)

Land use andbiodiversity(minimizes the impactson biodiversity ofspecies habitats andlandscapes)

Waste management(minimizes waste andimpact of wastes)

Alternative

Remanufacture VG G AG AP GRefurbishment MG MG G AP AGResell F F MP AP MPRepair F MG VG AP AGRecycle F MP VG AP AG

wm

•

3

efftto

4

a

1

Disposal AG AG G AG AG

here, S∗ = miniSi, S− = maxiSi, R∗ = miniRi, R− = maxiRi, and v is presented as weight of the strategy of “the majority of criteria” (or “theaximum group utility”), here suppose that v = 0.5.

Prioritize the alternatives. Ranking by the values S, R and Q in decreased order, in which the position in the front is better than that ofthe one behind.

.3. The expert elicitation step

In this step, the experts in the field of RL and green have been asked to express their technical views about the impacts of RL on greennvironmental factors, as presented in Table 3, and Table 4. In Table 3, the decision makers (experts) were asked to weigh environmentalactors based on their importance, by using the weights from Table 2. The most important item considered in weighting the environmentalactors is to weigh each factor without considering their integration with the reverse logistics functions. The aim of this consideration waso figure out how much each factor could be important in current environmental matters. Furthermore, the experts were asked to rankhe impacts of each reverse logistics’ decision option on each environmental factor by using the attribute value from Table 2. The resultsf these rankings are illustrated in Table 4.

. Results and discussion

According to the VIKOR method and the concept of generalized interval-valued trapezoidal fuzzy numbers, which was discussed in thebove, the following results are acquired.

Convert the linguistic terms into interval-valued trapezoidal fuzzy numbers, and then get:

[ ˜wkj]1×5 = [[(0.93, 0.98, 1.00, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)],[(0.58, 0.63, 0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)],[(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)],[(0.00, 0.00, 0.02, 0.07; 0.8), (0.00, 0.00, 0.02, 0.07; 1.0)],[(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)]]

[˜xij]6×5 =

⎡⎢⎢⎢⎢⎣

[(0.93, 0.98, 1.00, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)][(0.58, 0.63, 0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)][(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)][(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)]

[(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)][(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)]

1

•

34 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

[(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)],[(0.58, 0.63.0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)],[(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0],[(0.58, 0.63.0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)],[(0.17, 0.22, 0.36, 0.42; 0.8), (0.17, 0.22, 0.36, 0.42; 0.8)],[(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)],

[(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)],[(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)],[(0.17, 0.22, 0.36, 0.42; 0.8), (0.17, 0.22, 0.36, 0.42; 1.0)],[(0.93, 0.98, 1.00, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)],[(0.93, 0.98, 1.00, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)],[(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)],

[(0.00, 0.00, 0.00, 0.00; 0.8), (0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8), (0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8), (0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8), (0.00, 0.00, 0.00, 0.00; 1.0)],[(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)],

[(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)][(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)][(0.17, 0.22, 0.36, 0.42; 0.8), (0.17, 0.22, 0.36, 0.42; 1.0)][(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)][(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)][(1.00, 1.00, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)]

⎤⎥⎥⎥⎥⎦

Calculate the weighted decision making matrix:

[ ˜Vij]6×5 =

⎡⎢⎢⎢⎢⎣

[(0.86, 0.96, 1.00, 1.00; 0.8), (0.86, 0.96, 1.00, 1.00; 1.0)],[(0.54, 0.62, 0.80, 0.86; 0.8), (0.54, 0.62, 0.80, 0.86; 1.0)],[(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)],[(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)][(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)],[(0.93, 0.98, 1.00, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)],

,

[(0.42, 0.49, 0.74, 0.83; 0.8), (0.42, 0.49, 0.74, 0.83; 1.0)],[(0.34, 0.40, 0.64, 0.74; 0.8), (0.34, 0.40, 0.64, 0.74; 1.0)],[(0.19, 0.26, 0.46, 0.56; 0.8), (0.19, 0.26, 0.46, 0.56; 1.0)],[(0.34, 0.40, 0.64, 0.74; 0.8), (0.34, 0.40, 0.64, 0.74; 1.0)],[(0.10, 0.14, 0.29, 0.36; 0.8), (0.10, 0.14, 0.29, 0.36; 1.0)],[(0.58, 0.63, 0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)],

[(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)],[(0.23, 0.32, 0.53, 0.63; 0.8), (0.23, 0.32, 0.53, 0.63; 1.0)],[(0.05, 0.09, 0.21, 0.27; 0.8), (0.05, 0.09, 0.21, 0.27; 1.0)],[(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)],[(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)],[(0.23, 0.32, 0.53, 0.63; 0.8), (0.23, 0.32, 0.53, 0.63; 1.0)],

[(0.00, 0.00, 0.00, 0.00; 0.8)], [(0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8)], [(0.00, 0.00, 0.00, 0.00; 1.0)],

[(0.00, 0.00, 0.00, 0.00; 0.8)], [(0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8)], [(0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.00, 0.00; 0.8)], [(0.00, 0.00, 0.00, 0.00; 1.0)],[(0.00, 0.00, 0.02, 0.07; 0.8)], [(0.00, 0.00, 0.02, 0.07; 1.0)],

•

•

•

A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138 135

[(0.72, 0.78, 0.92, 0.97; 0.8), (0.72, 0.78, 0.92, 0.97; 1.0)][(1.00, 100, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)][(0.17, 0.22, 0.36, 0.42; 0.8), (0.17, 0.22, 0.36, 0.42; 1.0)][(1.00, 100, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)][(1.00, 100, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)][(1.00, 100, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)]

⎤⎥⎥⎥⎥⎦

Determine the positive ideal solution and the negative ideal solution:

˜V+

= [[(0.93, 0.98, 1.00; 0.8), (0.93, 0.98, 1.00, 1.00; 1.0)],[(0.58, 0.63, 0.80, 0.86; 0.8), (0.58, 0.63, 0.80, 0.86; 1.0)],[(0.32, 0.41, 0.58, 0.65; 0.8), (0.32, 0.41, 0.58, 0.65; 1.0)],[(0.00, 0.00, 0.02, 0.07; 0.8), (0.00, 0.00, 0.02, 0.07; 1.0)],[(1.00, 100, 1.00, 1.00; 0.8), (1.00, 1.00, 1.00, 1.00; 1.0)]]

˜V−

= [[(0.30, 0.40, 0.58, 0.65; 0.8), (0.30, 0.40, 0.58, 0.65; 1.0)],[(0.10, 0.14, 0.29, 0.36; 0.8), (0.10, 0.14, 0.29, 0.36; 1.0)],[(0.05, 0.09, 0.21, 0.27; 0.8), (0.05, 0.09, 0.21, 0.27; 1.0],[(0.00, 0.00, 0.00, 0.00; 0.8), (0.00, 0.00, 0.00, 0.00; 1.0)],[(0.17, 0.22, 0.36, 0.42; 0.8), (0.17, 0.22, 0.36, 0.42; 1.0]]

Calculate the weighted matrix and the COG of each attribute with respect to the positive ideal solution and the negative ideal solution(y, x):

[(y, x)V ]6×5 =

⎡⎢⎢⎢⎢⎣

[(0.3053, 0.9491), (0.3810, 0.9491)], [(0.3480, 0.6206), (0.4350, 0.6206)],[(0.3417, 0.7043), (0.4271, 0.7043)], [(0.3467, 0.5314), (0.4333, 0.5314)],[(0.3552, 0.4813), (0.5519, 0.4813)], [(0.3387, 0.3687), (0.4234, 0.3687)],[(0.3552, 0.4813), (0.5519, 0.4813)], [(0.3467, 0.5314), (0.4333, 0.5314)],[(0.3552, 0.4813), (0.5519, 0.4813)], [(0.3436, 0.2235), (0.4295, 0.2235)],[(0.3048, 0.9745), (0.3810, 0.9745)], [(0.3476, 0.7179), (0.4345, 0.7179)],

[(0.3354, 0.4892), (0.4192, 0.4892)], [(0.40, 0.00), (0.50, 0.00)],[(0.3367, 0.4279), (0.4208, 0.4279)], [(0.40, 0.00), (0.50, 0.00)],[(0.3394, 0.1558), (0.4242, 0.1558)], [(0.40, 0.00), (0.50, 0.00)],[(0.3352, 0.4814), (0.4190, 0.4814)], [(0.40, 0.00), (0.50, 0.00)],[(0.3352, 0.4814), (0.4190, 0.4814)], [(0.40, 0.00), (0.50, 0.00)],

[(0.3367, 0.4279), (0.4208, 0.4279)], [(0.3048, 0.0255), (0.3810, 0.0255)],

[(0.3413, 0.8741), (0.4267, 0.8471)][(0.4000, 1.0000), (0.5000, 1.0000)][(0.3413, 0.2929), (0.4267, 0.2929)][(0.4000, 1.0000), (0.5000, 1.0000)][(0.4000, 1.0000), (0.5000, 1.0000)][(0.4000, 1.0000), (0.5000, 1.0000)]

⎤⎥⎥⎥⎥⎦

[(y, x)V+ ]5 =[[(0.3048, 0.9745), (0.3810, 0.9745)], [(0.3476, 0.7179), (0.4345, 0.7179)],[(0.3354, 0.4892), (0.4192, 0.4892)], [(0.3048, 0.0255), (0.3810, 0.0255)],[(0.4000, 1.0000), (0.5000, 1.0000)]]

[(y, x)V− ]5 =[[(0.3352, 0.4814), (0.4190, 0.4814)], [(0.3436, 0.2235), (0.4295, 0.2235)],[(0.3394, 0.1558), (0.4242, 0.1558)], [(0.4000, 0.0000), (0.5000, 0.0000)],[(0.3413, 0.2929), (0.4267, 0.2929)]]

Compute the values Si and Ri, i = 1, 2, 3, 4, 5, 6.

S1 = 1.4831, S2 = 2.1145, S3 = 4.7322, S4 = 2.4289, S5 = 3.0516, S6 = 0.1841

R1 = 1, R2 = 1, R3 = 1.0283, R4 = 1.0283, R5 = 1.0283, R6 = 0.1841

136 A. Haji Vahabzadeh et al. / Resources, Conservation and Recycling 103 (2015) 125–138

Table 5Final ranking of alternatives in VIKOR method.

Si Ri Qi Rank

Remanufacture (a1) 1.4831 1 0.626 2Refurbishment (a2) 2.1145 1 0.6954 3Resell (a3) 4.7322 1.0283 1 6Repair (a4) 2.4289 1.0283 0.7468 4

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Recycle (a5) 3.0516 1.0283 0.8152 5Disposal (a6) 0.1841 0.1841 0 1

Compute the values Qi, i = 1, 2, 3, 4, 5, 6.

Q1 = 0.626, Q2 = 0.6954, Q3 = 1, Q4 = 0.7468, Q5 = 0.8152, Q6 = 0

Rank the alternatives based on the value of Q, R, and S:

a6 > a1 > a2 > a4 > a5 > a3

According to the final computations (Table 5), the disposal recovery option turned out to be the best proposed option as it has theinimum Qi; thereby the lowest negative impact on the environment. The resell recovery option on the other hand was identified as

he worst proposed option, with the highest Qi, as well. Consequently, the results obtained from the elicitation of the experts ranked thelternatives and verified the proposed decision making model.

. Conclusion

This paper makes an attempt to fill the literature gap on identification and validation and prioritization of green decision making specifico reverse logistics in a fuzzy environment that will ultimately contribute to the conservation of resources. It was argued that the lack of

concise and comprehensive elaboration in the impact analysis of RL recovery options on the green environmental factors motivated theuthors to undertake this research. To cope with the presented issue, the FUZZY-VIKOR method is proposed. In the current approach, theeneralized interval-valued trapezoidal fuzzy numbers are employed to quantify the linguistic terms used in the ranking method throughhe elicitation of experts. In order to prioritize the greenest recovery options in RL, the VIKOR method was also used. According to the finalesults, disposing and reselling the returns are ranked as the best and worst alternatives in terms of the green metric, respectively.

In addition, from the methodological point of view, it is important to note that one of the biggest challenges in translating the practicento an applicable model is to use a reliable method that is able to precisely reflect the reality of each factor in the model as they existn the practice. The approach of Fuzzy logic together with the VIKOR method assisted the researchers in providing results that are verylose to the real world. To conclude, the findings from this study offer managers an audit tool of how and what to deploy with respect toeverse logistics efforts. One particular pragmatic tool that can be offered is to test the viability of the different reverse logistics activitiese.g. disposing and reselling) by way of focused process improvement projects that are aimed at improving sustainability.

.1. Recommendations for further research

There are a lot of opportunities for future works. First, one of the limitations in this research was to only examine the impacts of greennvironmental factors on the RL recovery options. While from the managerial point of view, it would be interesting to study a sustainableeverse logistics through the proposed methodology. Therefore, the future works could identify and rank the economic and societal factorsf RL that affect the final recovery options as well and flowingly apply the same approach presented in this work. However, it is critical tohoose the most primary factors that affect the choice of final decision; otherwise the computations might be complex and the analysisay become cumbersome. To avoid any difficulties that might be experienced in this regard, we suggest to the researchers to apply aulti-stage decision making model. Second, in this study, we have only conducted the interviews with the experts in the manufacturer

ompanies, however, as different parties are involved in the RL cycle, the analyses would be more realistic if we could reflect the technicalpinions of other decision makers in RL (e.g., third-party reverse logistics providers, suppliers and customers). Although the influences ofesigning the green products (Khor and Udin, 2013) or transportation on returns have been discussed in the literature, almost no researchas explicitly argued the influences of a group decision making across the RL on the best recovery option. This requires that managersesign a clear and cost-effective policy that thoroughly encompasses the needs and expectations of all the involved parties in RL. In ordero maintain an efficient policy, it is essential that the critical metrics defined, measured, monitored and more importantly shared among allhe stakeholders. Finally, another direction for the future research would be to apply some other Fuzz-MADM methods such Fuzzy-TOPSISr Fuzzy-DEMATEL and compare the results of them with our results.

cknowledgment

Thank you to all the authors listed in the references and to all the reviewers for their constructive comments.

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