SPHERICAL FUZZY SWARA-MARCOS APPROACH FOR GREEN SUPPLIER SELECTION

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INTRODUCTION
Supply chains are of great importance for businesses to maintain their main activities (Stevens, 1989).For the establishment and proper functioning of supply chains, the appropriate supplier must be selected.The criteria (attributes) to be considered when choosing a supplier often conflict with each other and cause difficulty in decision making (Akcan & Taş, 2019).Multi-criteria decision-making methods (MCDM) can be used to overcome these difficulties.These methods help to evaluate alternatives using criteria with different characteristics (De Boer et al., 2001).In addition, it is appropriate to use fuzzy sets for imprecise statements of decision makers.These methods are frequently used in supplier selection practices (Yazdani et al., 2017).In recent years, thanks to the increase in environmental awareness, sustainable supply chain has gained importance.Therefore, the concept of green supply chain that cares about the environment has emerged (Bali et al., 2013).Sustainable criteria should be taken into account and determined as environmental performance evaluations.Using the MCDM methods, the suitable supplier in the green supply chain can be determined according to the sustainable criteria.Various MCDM have been used for green supplier selection in the literature, including some methods such as AHP (Mavi, 2015), PROMETHEE (Govindan et al., 2017), TOPSIS (Cao et al., 2015), ANP (Chung et al., 2016), DEA (Dobos & Vörösmarty, 2019), VIKOR (Akman, 2015), ELECTRE (Kumar et al, 2017), COPRAS (Liou, 2016), DEMATEL (Hsu, 2013), EDAS (He, 2019), TODIM (Sang & Liu, 2016), WASPAS (Ghorabaee, 2016), MULTIMOORA (Sen et al., 2017), and more.In this study, SWARA and MARCOS are combined with spherical fuzzy sets (SFS) for fuzzy MCDM problems.
SWARA method was introduced to the literature by Keršuliene et al. (2010).The method was applied to evaluate the criteria for the selection of agile supplier of an automobile manufacturer in Iran (Alimardan et al., 2013), the evaluation of investments in high technology sectors (Hashemkhani & Bahrami, 2014), the design of bottle package (Stanujkic et al., 2015), the selection of renewable energy technology (Ijadi Maghsoodi et al., 2018), the appraisal of sustainable properties for renewable energy systems (Ghenai et al., 2020).
"In spherical fuzzy numbers, while the squared sum of membership, non-membership and hesitancy parameters can be between 0 and 1, each of them can be defined between 0 and 1 independently to satisfy that their squared sum is at most equal to 1" (Gündoğdu & Kahraman, 2019b).Additionally, this study proposes a new spherical fuzzy-SWARA combination to the literature.
The Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method is first introduced to the literature by Stević et al. (2020).Ilieva et al. researched on the manual stacker selection for small warehouses, using CCSD, ITARA, and MARCOS.They used the MARCOS to evaluate the alternatives.Puška et al. (2020) performed MARCOS in selection of project management software.
In this study examines the green supplier selection problem of a textile firm.To examine environmental performance, twelve green criteria are determined.Seven decision makers (DM) working within the company evaluate the criteria and alternatives with the spherical fuzzy numbers.The weights of the criteria are calculated by the spherical fuzzy-SWARA method.Applying the steps of the MARCOS, the alternatives are ranked.In the lights of the literature review, the original contribution of this study is that the proposed methodology is the pioneering work that combines spherical fuzzy-SWARA and MARCOS method.In addition, the proposed methodology is adapted to a real-life problem by investigating a green supplier selection case.
The rest of the paper is organized as follows.The preliminaries and definitions of the spherical fuzzy sets are given in Section 2. The proposed methodology involving the original combination of the spherical fuzzy-SWARA and MARCOS methods are also introduced in Section 2. Section 3 applies the proposed methodology on a green supplier selection case and a sensitivity analysis is applied for different weighting criteria scenarios.Finally, conclusion and future perspectives are discussed in Section 4.

PROPOSED METHODOLOGY
In this section, the steps of combined the spherical fuzzy-SWARA and MARCOS methods are introduced.Firstly, the spherical fuzzy-SWARA method is given to calculate the weights of the criteria and then, MARCOS (Stević et al., 2020) method is applied to rank of the alternatives.This study implements the spherical fuzzy sets to SWARA (Stanujkic et al., 2015) steps as follows: Step 1. Set the problem and select the experts/decision makers according to the problem.Step 2. Ranking the criteria by the spherical fuzzy-SWARA.Criteria are ranked based on DM evaluations.The ranking is from highest importance to lowest.
Step 3.1.Extend the initial decision matrix.Ideal (AI) and Anti-ideal (AAI) solutions are included to the matrix.Ideal (AI) solution is the best alternative.The below is the expression of ideal (AI) solution (Eq.11): Anti-ideal (AAI) solution is the worst alternative.The expression of anti-ideal (AAI) solution (Eq.12) is as follows: (12) Here, C symbolizes cost criteria to be minimized, whereas B symbolizes benefit criteria to be maximized.The extended decision matrix (X) is shown below: Step 3.2.Normalize of matrix "X" with Eq. ( 13) and ( 14) for benefit criteria and cost criteria, respectively.x ij and x ai belong to matrix "X".
(13) (14) Step 3.3.Creating the weighted matrix "V" using Eq. ( 15).w j values represent criteria weights which are calculated or determined. (15) Step 3.4.Calculate the S i and K i .S i stands for the sum of v ij and K i stands for the utility degree of alternatives.The values are calculated using Eq. ( 16), ( 17) and (18) below.
( ) and f(K i -) are used for the utility function with respect to the ideal and anti-ideal solution, respectively.These values are calculated using Eq. ( 19), ( 20) and ( 21 Step 3.6.Create the ranking of alternatives.
Step 4. Determining the best alternative which is the one with the highest score.

CASE STUDY
A textile manufacturer located in Marmara region in Turkey is selected as a case study of proposed model.The firm operates in the international market.Twelve sustainable criteria have been determined for the evaluation of six alternative suppliers, which supply raw materials.These green criteria are given in Table 2.The criteria C 7 , C 11 and C 12 are cost type, the others are benefit type.The spherical fuzzy-SWARA steps are implemented based on the assessment of each of the seven DM from the company.The importance order of the criteria is given in Table 3.The results are combined by taking the arithmetic mean of the results for seven decision makers and the final criteria weights are calculated as in Table 4.   Avg.

CONCLUSIONS
Nowadays, organizations are expected to be environmentally friendly in their supply chains.
Therefore, selecting suitable green suppliers in sustainable supply chains is a very important task.In this study, the green supplier selection problem of a textile company is investigated.
The spherical fuzzy-SWARA and MARCOS methods are handled in an integrated way.As a result of the combined spherical fuzzy-SWARA method, the highest weight criteria are green image, environmental management system and green transportation, respectively.
According to the MARCOS method, the best green supplier is A 2 and the ranking of alternatives is A 2 >A 3 >A 5 >A 4 >A 1 >A 6 .Subsequently, for different scenarios, alternative suppliers are ranked, and the results are compared.Consequently, it is clear that the results of the proposed methodology is consistent.For future studies, the other fuzzy extentions of fuzzy sets can be considered in expressing the views of DMs, and new fuzzy MCDM methods should be implemented for sustainable supply chain problems.

( 2020 )
used fuzzy MARCOS for ordering cloud storage service.Chattopadhyay et al. (2020) conducted a supplier selection study for the iron and steel industry using D-MARCOS.Stević and Brković (2020) used integrated FUCOM-MARCOS methodology to evaluate the human resources of the transportation company and to select the employee of the month.Stanković et al. (2020) studied on the risks of the main road with the fuzzy MARCOS.Badi and Pamucar (2020) used MARCOS with gray numbers in the supplier selection of Libyan Iron and Steel Company.Vesković et al. (2020) assessed possible solutions to problems of railway transportation in Republic of Srpska.F-MARCOS was chosen as one of the MCDM methods to compare the results.Mijajlović et al. (2020) employed FUCOMand fuzzy MARCOS to examine the competition of spa centers.Ulutaş et al. (2020)

Table 1 .
Linguistic measures of importance used for comparison.

Table 2 .
The green criteria for textile manufacturer supplier selection.

Table 3 .
The orders of importance.

Table 5 .
The extended initial decision matrix "X".
Source: own elaboration.Figure 2. The ranking Scores of Alternatives.Source: own elaboration.