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SPHERICAL FUZZY SWARA-MARCOS APPROACH FOR
GREEN SUPPLIER SELECTION
Mehmet Ali Taş
Department of Industrial Engineering, Turkish-German University.
Istanbul, (Turkey).
E-mail: mehmetali.tas@tau.edu.tr
ORCID: https://orcid.org/0000-0003-3333-7972
Esra Çakır
Department of Industrial Engineering, Galatasaray University
Istanbul, (Turkey).
E-mail: ecakir@gsu.edu.tr
ORCID: https://orcid.org/0000-0003-4134-7679
Ziya Ulukan
Department of Industrial Engineering, Galatasaray University
Istanbul, (Turkey).
E-mail: zulukan@gsu.edu.tr
ORCID: https://orcid.org/ 0000-0003-4805-2726
Recepción:
01/12/2020
Aceptación:
22/02/2021
Publicación:
07/05/2021
Citación sugerida:
Taş, M. A., Çakır, E., y Ulukan, Z. (2021). Spherical fuzzy SWARA-MARCOS approach for green
supplier selection. 3C Tecnología. Glosas de innovación aplicadas a la pyme, Edición Especial, (mayo 2021), 115-
133. https://doi.org/10.17993/3ctecno.2021.specialissue7.115-133
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ABSTRACT
In a supply chain management, supplier selection is an important step to determine the
structure of the model. Multi-criteria decision making methods are appropriate tools for
dealing with the selection of suitable suppliers. In addition, fuzzy multi-criteria decision
making approaches are helpful to include dierent and uncertain views of decision makers.
In this study, a new combined fuzzy methodology is proposed to handle green supplier
selection problem. The proposed model consists of a spherical fuzzy-SWARA method,
which is used to calculate the criteria weights, and MARCOS method, which is applied
to rank the alternatives. In the case study, green supplier selection problem of a textile
company located in Turkey is discussed. Six alternative suppliers are evaluated against
twelve green criteria, and alternatives are ranked. Finally, a sensitivity analysis is performed
to compare the results of dierent scenarios.
KEYWORDS
Green supplier selection, MARCOS, MCDM, Spherical fuzzy sets, Supply chain, Spherical
fuzzy - SWARA.
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1. 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 conict with each other and cause diculty in decision making
(Akcan & Taş, 2019). Multi-criteria decision-making methods (MCDM) can be used to
overcome these diculties. These methods help to evaluate alternatives using criteria with
dierent 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).
After Zadeh (1965) introduce the ordinary fuzzy sets, numerous extensions have been
proposed such as type-2 fuzzy sets (Zadeh, 1975), intuitionistic fuzzy sets (Atanassov,
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1986), hesitant fuzzy sets (Torra, 2010), Pythagorean fuzzy sets (Yager, 2013), neutrosophic
fuzzy sets (Smarandache, 1998), and so on. In the literature, many research combined
SWARA and fuzzy sets. Some of these are those: ordinary fuzzy-SWARA (Perçin, 2019),
hesitant fuzzy-SWARA (Kaya & Erginel, 2020), symmetric interval type-2 fuzzy-SWARA
(Keshavarz-Ghorabaee, 2018), neutrosophic fuzzy-SWARA (Rani & Mishra, 2020). In
2018, as an extension of fuzzy sets, spherical fuzzy numbers are introduced (Gündoğdu &
Kahraman, 2019a). These fuzzy sets dier from others in that they are three-dimensional.
“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 dened 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 rst introduced to the literature by Stević et al. (2020). Ilieva et al.
(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 FUCOM
and fuzzy MARCOS to examine the competition of spa centers. Ulutaş et al. (2020)
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 rm. 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
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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 denitions 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 dierent weighting criteria scenarios. Finally,
conclusion and future perspectives are discussed in Section 4.
2. METHODOLOGY
2.1. PRELIMINARIES
This section gives the preliminaries and denitions of the proposed method with spherical
fuzzy information (Gündoğdu & Kahraman, 2019a; Gündoğdu & Kahraman, 2019b):
Denition 1: A spherical fuzzy set à of the universe of discourse X is given by:
(1)
The μ
Ã
(x), η
Ã
(x) and v
Ã
(x) represent membership degree, non-membership
degree and hesitancy of x to Ã, respectively and they satisfy the condition
. The hesitancy parameter of
à is expressed as π
Ã
(x)= . The expression (μ
Ã
(x), η
Ã
(x), v
Ã
(x)) is simply called the spherical fuzzy number (SFN), which can be represented as α = (μ,
η, v). In Figure 1, the spherical fuzzy set is illustrated.
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Figure 1. Geometric representation of SFS.
Source: (Gündoğdu & Kahraman, 2019b).
Denition 2: Let α
1
= (μ
1
, η
1
, v
1
) and α
2
= (μ
2
, η
2
, v
2
) be two SFN and let λ be a positive real
number, then:
(2)
(3)
(4)
(5)
The complement of the spherical fuzzy number α = (μ, η, v) is dened as follows:
α
C
= (v, η, μ) (6)
2.2. 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.
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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 2.1. Determine s ̃
j
value: s ̃
j
is named “comparative importance of average value”
by linguistic measures in Table 1.
Table 1. Linguistic measures of importance used for comparison.
Linguistic measures (μ, η, v)
Equally Importance (EI) (0.5, 0.4, 0.4)
Slightly Low Importance (SLI) (0.4, 0.6, 0.3)
Low Importance (LI) (0.3, 0.7, 0.2)
Very Low Importance (VLI) (0.2, 0.8, 0.1)
Absolutely Low Importance (ALI) (0.1, 0.9, 0.0)
Source: (Gündoğdu & Kahraman, 2019b).
Step 2.2. Determine k ̃
j
coecient: k ̃
j
coecient is calculated using Eq. (7):
(7)
Step 2.3. Calculate the scores of k ̃
j
coecient: the scores of the k ̃
j
is calculated with
Eq. (8):
(8)
Step 2.4. Determine q
j
value: The importance vector value q
j
is calculated with Eq. (9):
(9)
Step 2.5. Determine w
j
value: w
j
values are the weights of the criteria, which is calculated
using Eq. (10):
(10)
Step 3. Ranking the criteria by MARCOS (Stević et al., 2020). Creating an initial decision
matrix.
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):
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(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 benet 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 benet 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.
(16)
(17)
(18)
X
=
AAI
A
1
...
A
m
AI
x
aa1
x
11
...
x
m1
x
ai1
x
aan
x
1n
...
x
mn
x
ain
...
...
...
...
...
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Step 3.5. Formulate the utility function. f(K
i
+
) 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) below.
(19)
(20)
(21)
Step 3.6. Create the ranking of alternatives.
Step 4. Determining the best alternative which is the one with the highest score.
3. CASE STUDY
A textile manufacturer located in Marmara region in Turkey is selected as a case study of
proposed model. The rm 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.
Table 2. The green criteria for textile manufacturer supplier selection.
Code Criterion Code Criterion
C
1
Environmental management system C
7
Resource/energy consumption
C
2
Green packaging C
8
Green design
C
3
Green transportation C
9
Green technology
C
4
Green image C
10
Green purchasing
C
5
Staff environmental management C
11
Pollution production
C
6
Green warehousing C
12
Waste water
Source: own elaboration.
The criteria C
7
, C
11
and C
12
are cost type, the others are benet 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
nal criteria weights are calculated as in Table 4.
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Table 3. The orders of importance.
Order DM
1
DM
2
DM
3
DM
4
DM
5
DM
6
DM
7
1 C
4
C
3
C
1
C
7
C
7
C
10
C
1
2 C
8
C
6
C
4
C
4
C
3
C
2
C
9
3 C
1
C
2
C
5
C
3
C
4
C
3
C
4
4 C
6
C
1
C
7
C
1
C
9
C
4
C
3
5 C
2
C
4
C
8
C
2
C
2
C
1
C
11
6 C
9
C
10
C
10
C
8
C
1
C
7
C
8
7 C
3
C
7
C
11
C
10
C
11
C
9
C
2
8 C
5
C
11
C
2
C
11
C
5
C
8
C
6
9 C
10
C
12
C
9
C
12
C
12
C
12
C
7
10 C
11
C
5
C
3
C
9
C
8
C
6
C
5
11 C
7
C
8
C
6
C
6
C
10
C
11
C
10
12 C
12
C
9
C
12
C
5
C
6
C
5
C
12
Source: own elaboration.
Table 4. The spherical fuzzy-SWARA results.
C
n
DM
1
DM
2
DM
3
DM
4
DM
5
DM
6
DM
7
Avg. Ranking Results
C
1
0,1072 0,1029 0,1575 0,0959 0,0853 0,0946 0,1572 0,1144 2
C
2
0,0851 0,1132 0,0636 0,0872 0,0896 0,1095 0,0746 0,0890 4
C
3
0,0736 0,1627 0,0551 0,1007 0,1087 0,1043 0,1081 0,1019 3
C
4
0,1356 0,0936 0,1432 0,1158 0,1035 0,0993 0,1243 0,1165 1
C
5
0,0701 0,0452 0,1061 0,0565 0,0739 0,0383 0,0398 0,0614 11
C
6
0,1021 0,1302 0,0501 0,0621 0,0580 0,0543 0,0622 0,0741 9
C
7
0,0528 0,0740 0,0964 0,1216 0,1141 0,0822 0,0518 0,0847 5
C
8
0,1232 0,0430 0,0877 0,0793 0,0640 0,0746 0,0783 0,0786 7
C
9
0,0810 0,0391 0,0578 0,0652 0,0941 0,0783 0,1429 0,0798 6
C
10
0,0610 0,0851 0,0701 0,0755 0,0609 0,1533 0,0362 0,0774 8
C
11
0,0581 0,0569 0,0668 0,0719 0,0776 0,0517 0,0901 0,0676 10
C
12
0,0503 0,0542 0,0455 0,0685 0,0704 0,0597 0,0345 0,0547 12
Tot. 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000
Source: own elaboration.
In Step 3, MARCOS method is performed to evaluate the suppliers (A
1
, A
2
, A
3
, A
4
, A
5
,
A
6
) by using the criteria weights. The extended initial decision matrix “X” and normalized
weighted matrix “V” are shown in Table 5 and Table 6.
Table 5. The extended initial decision matrix “X”.
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
Weights 0,1144 0,0890 0,1019 0,1165 0,0614 0,0741 0,0847 0,0786 0,0798 0,0774 0,0676 0,0547
Type max max max max max max min max max max min min
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Source: own elaboration.
In the Step 3.4 with the help of the values from Table 4, S
i
, K
i
+
and K
i
-
values are calculated
by Equations (16), (17), and (18). In Step 3.5, f(K
i
) values are found for utility functions and
scores of alternatives are calculated by Equations (19), (20), and (21). The scores of the
alternative suppliers (A
1
, A
2
, A
3
, A
4
, A
5
, A
6
) are shown in Figure 2. According to the results
of MARCOS method, the best alternative of green supplier is A
2
with the highest score.
Second one is A
3
, and third is A
5
.
Table 6. Normalized weighted matrix “V”.
Source: own elaboration.
Figure 2. The ranking Scores of Alternatives.
Source: own elaboration.
AAI 3,7143 3,1429 2,1429 2,1429 4,5714 4,0000 7,2857 4,0000 3,8571 1,8571 8,1429 6,8571
A
1
3,8571 5,2857 3,0000 4,2857 7,5714 4,7143 3,2857 5,0000 3,8571 6,7143 6,7143 5,0000
A
2
5,0000 5,2857 5,1429 4,0000 6,8571 4,4286 3,0000 5,0000 5,1429 7,0000 3,8571 6,1429
A
3
5,4286 3,2857 5,0000 6,4286 5,0000 6,4286 7,2857 4,8571 8,4286 8,1429 8,1429 6,8571
A
4
6,7143 5,8571 2,1429 6,1429 4,5714 5,4286 4,7143 6,1429 4,1429 1,8571 5,1429 5,2857
A
5
3,7143 3,1429 5,0000 7,5714 7,7143 8,1429 7,0000 4,2857 5,0000 3,8571 3,5714 2,7143
A
6
4,4286 4,1429 3,4286 2,1429 6,5714 4,0000 4,5714 4,0000 4,7143 5,0000 1,5714 4,5714
AI 6,7143 5,8571 5,1429 7,5714 7,7143 8,1429 3,0000 6,1429 8,4286 8,1429 1,5714 2,7143
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
AAI 0,0633 0,0477 0,0425 0,0330 0,0364 0,0364 0,0349 0,0512 0,0365 0,0177 0,0130 0,0217
A
1
0,0657 0,0803 0,0594 0,0659 0,0603 0,0429 0,0773 0,0640 0,0365 0,0639 0,0158 0,0297
A
2
0,0852 0,0803 0,1019 0,0615 0,0546 0,0403 0,0847 0,0640 0,0487 0,0666 0,0275 0,0242
A
3
0,0925 0,0499 0,0991 0,0989 0,0398 0,0585 0,0349 0,0621 0,0798 0,0774 0,0130 0,0217
A
4
0,1144 0,0890 0,0425 0,0945 0,0364 0,0494 0,0539 0,0786 0,0392 0,0177 0,0206 0,0281
A
5
0,0633 0,0477 0,0991 0,1165 0,0614 0,0741 0,0363 0,0548 0,0473 0,0367 0,0297 0,0547
A
6
0,0754 0,0629 0,0679 0,0330 0,0523 0,0364 0,0556 0,0512 0,0446 0,0476 0,0676 0,0325
AI 0,1144 0,0890 0,1019 0,1165 0,0614 0,0741 0,0847 0,0786 0,0798 0,0774 0,0676 0,0547
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To perform a sensitivity analysis of the proposed methodology, thirteen dierent scenarios
are created by changing the weights of the criteria and the results are compared. According
to the results, A
2
is the rst and A
6
is the last in the ranking in all thirteen scenarios. Although
ranking results changes in four scenarios, it is generally the same as the results of combined
the spherical fuzzy-SWARA-MARCOS method.
Figure 3. Comparison of different scenarios.
Source: own elaboration.
4. 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 dierent 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.
0,6600
0,6400
0,6200
0,6000
0,5800
0,5600
0,5400
S0 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
S12 S13
A1
A2 A3 A4 A5 A6
S11
Ave.
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5. ACKNOWLEDGEMENTS
This work has been supported by the Scientic Research Projects Commission of
Galatasaray University under grant number # FBA-2020-1036.
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