RESEARCH ARTICLE

A novel spherical fuzzy AHP-integrated spherical WASPASmethodology for petrol station location selection problem: a realcase study for İstanbul

Ertugrul Ayyildiz1 & Alev Taskin Gumus1

Received: 23 April 2020 /Accepted: 8 June 2020# Springer-Verlag GmbH Germany, part of Springer Nature 2020

AbstractThe petrol station location selection problem is taken into consideration in this study. In order to identify the main and sub-criteriafor evaluation, the literature is reviewed and five experts from different companies are interviewed. After that, thirteen differentalternative locations are for specified to evaluation. Then, the novel spherical fuzzy AHP-integrated spherical WASPAS meth-odology is structured in a fuzzy environment, and the petrol station location selection problem is evaluated with this methodol-ogy. In this study, a real application is presented for Istanbul to show the applicability of the proposed methodology.Subsequently, a sensitivity analysis is performed to explain and analyze the proposed methodology results. Finally, the resultsare presented and discussed with future directions.

Keywords Location selection . Petrol station . Spherical fuzzy . AHP .WASPAS

Introduction and related studies

Researchers, theoreticians and practitioners have focused onfacility location selection problem and its extension over theyears (Chabuk et al. 2019; M. Eskandari et al. 2015; MahnazEskandari et al. 2016; Gwak et al. 2017; Man et al. 2020;Tuzkaya et al. 2008). Facilities are located at the most appro-priate locations to minimize or maximize objective consider-ing several constraint sets (Aragonés-Beltrán et al. 2010; Deyand Ramcharan 2008; Koc et al. 2019; Solangi et al. 2019;Soroudi et al. 2018; Vahidnia et al. 2009). Researchers handleand solve this problem by developing different decision sup-port models such as optimization, multicriteria decision-mak-ing, etc. The number of applications of this problem for thepublic and private sectors is increasing day by day.

The petrol station location selection problem is one of thefacility location selection problem application areas. The us-age of petrol increases every day with the rapid developmentof the economy when focusing on the petrol market. Petrol isused for transportation, energy, etc. Petrol can be classified aswhite, black, and aviation fuel in the oil refining and distribu-tion sector. White products are generally used in motor vehi-cles, black products are used in heating and industry. Whitepetrol is usually supplied by petrol stations and used for trans-portation. In this context, meeting customer demand is veryimportant for the petrol market; therefore, petrol station loca-tion selection plays a key role.

The most important decision to be made by the petrolstation investor is determining the location of the facility(Wang and Wang 2010), because the advantages and disad-vantages of the selected location are important factors thatdetermine the sales volume of the station (Galankashi et al.2018). This determines the investor’s ability to compete.Not making the right decision on the location selectionmay lead to irreversible bad results (Daskin et al. 2005). Itis very hard to compensate for the lost cost. On the otherhand, the location selection and licensing stages of petrolstations in the zoning plan are the most frequently encoun-tered problems of local administrations.

One of the most important factors running the petrol stationinvestors into difficulty in Turkey is that the construction

Responsible editor: Marcus Schulz

* Ertugrul Ayyildizeayildiz@yildiz.edu.tr

Alev Taskin Gumusataskingumus@gmail.com

1 Department of Industrial Engineering, Yildiz Technical University,Istanbul, Turkey

https://doi.org/10.1007/s11356-020-09640-0

/ Published online: 17 June 2020

Environmental Science and Pollution Research (2020) 27:36109–36120

plans depend on many criteria. Providing the necessary con-dition for the petrol station is quite difficult in metropolitancities such as Istanbul. Transportation and firefighting are dif-ficult in crowded cities. Also, the adaptation of petrol stationsto land is important for infrastructure systems. Natural disas-ters should also be considered by law when determining thelocations of petrol stations. Another issue that the investor hasto decide is to select the best region for the petrol station wherethe sales volume can be the highest, considering the high taxrates in the sector and the size of the investment to be made.The investor must decide by considering more than onecriteria while determining the location for the facility (Kloseand Drexl 2005). Multicriteria decision-making methods arethe most used methods in such conditions (Ozcelik et al.2014). The number of studies about location selection prob-lem and its extensions is increasing. But there is a limitednumber of studies about the petrol station location selectionproblem.

Upchurch et al. (2009) present a capacitated location modelfor a petrol station that has several limitations related to thenumber of vehicles. Lim and Kuby (2010) developmultialgorithms to determine the best location for the petrolstation that sells alternative fuels such as hydrogen, ethanol,electricity, and biodiesel. MirHassani and Ebrazi (2013) refor-mulate the petrol station location selection problem. They de-veloped a mixed integer linear programming model as a ver-sion of the set covering problem. Montoya et al. (2016) deter-mine the locations of petrol stations using a novel heuristic.They formulate the problem as a green vehicle routing prob-lem. Khahro and Memon (2017) use geographic informationsystem (GIS) to find the most appropriate land for the petrolstation. Determining best location for petrol station via opti-mization techniques, which are minimizing the risk or cost, isthe studied topic in the literature. But there is a limited numberof studies on defining criteria and determining weights ofcriteria for the petrol station location selection problem.Apart from the other studies, the problem is handled as amulticriteria decision-making problem. In this context, thisstudy stands out as the most detailed study in which all thecriteria in the process are defined and evaluated comprehen-sively. In addition, it is the first study that solves this problemin a fuzzy environment.

The present study reviews the related literature, defines themain and sub-criteria in a hierarchical structure for the prob-lem of petrol station location selection, gains opinions of mul-tiple experts, and analyzes their opinions by applying the pro-posed novel spherical fuzzy analytical hierarchy process(AHP)-integrated spherical fuzzy weighted aggregated sum-product assessment (WASPAS) methodology. The impor-tance weights of considered criteria and evaluation of speci-fied candidate locations are also determined by the proposedmethodology. A real case study for İstanbul is performed toshow the applicability of the proposed methodology.

AHP is based on the pairwise comparison of criteria andalternatives considering the objective values and/or subjectiveopinions (Çavdur et al. 2019; Yerlikaya and Arikan 2016).The method is one of the most used multicriteria decision-making methods. Even the method collects information fromexperts, sometimes it may not reflect the opinions taken frompeople accurately. Therefore, AHP is combined with fuzzylogic and fuzzy AHP is emerged to overcome this problem(Ayyildiz et al. 2020).

Zadeh presented the theory of fuzzy logic to the literature,firstly (Zadeh 1965). The fuzzy logic theory is applicable toboth qualitative assessment and subjective judgment for thedecision-making problems. The rationality of uncertainty dueto ambiguity plays a key role in fuzzy logic. In order to handleuncertainty in information, the linguistic approach is used (J. Q.Wang et al. 2015). The comparison is performed using a rangeof values in fuzzy AHP, unlike the traditional AHP that netvalues are used (Ayyildiz et al. 2020). The multicriteriadecision-making problems consist of multiple linguistic criteriato perform a better decision-making process. These linguisticcriteria can be defined using different fuzzy sets. Type-2 fuzzysets (Zadeh 1975), intuitionistic fuzzy sets (Atanassov 1999),hesitant fuzzy sets (Torra 2010), pythagorean fuzzy sets (Yager2013), and neutrosophic fuzzy sets (Smarandache 1999) are themost used fuzzy sets to define linguistic criteria. A sphericalfuzzy sets (SFS) can also be used to realize the criteria to handleambiguity and fuzziness in linguistic expressions. SFS are anew viewpoint to decision-making in a fuzzy environment(Gündoǧdu and Kahraman 2019). The indeterminacy level ofthe decision maker is defined independently from membershiplevel and nonmembership level of element in these sets. In SFS,decision makers define membership function on a sphericalsurface to generalize other fuzzy sets. So they assign the param-eters of this membership function in a larger domain(Gündoǧdu and Kahraman 2019). SFS are a combination ofpythagorean fuzzy sets with neutrosophic fuzzy sets.

The usage of the AHP method, which is based on humanjudgments in decision-making problems, increased consider-ably recently in the literature. The applications of differentversions of fuzzy AHP by integrating it with other decision-making methods are increasing day by day. Table 1 showssome remarkable studies on different versions of fuzzy AHPintegration with different decision-making methods.

WASPAS method is famous and efficient to solvemulticriteria decision-making problems. The original ideasof WASPAS method are first merely published in 2012(Zavadskas et al. 2012). WASPAS is briefly a combinationof weighted total and weighted multiplication methods, whichare multicriteria decision-making techniques.

This study is organized as follows: the proposed novelmethodology is presented in the “The proposedmethodology”section. The “The numerical application for İstanbul” sectiongives the real case study and sensitivity analysis of the

36110 Environ Sci Pollut Res (2020) 27:36109–36120

proposed methodology. Lastly, the conclusions and futurerecommendations are given in the “Conclusion and futuredirections” section.

The proposed methodology

In this study, WASPAS method is integrated with the AHPmethod. Spherical fuzzy numbers are used in order to betterrepresent fuzziness and ambiguity in information, here.Before the outlines of the proposed decision-making methodon the proposed hybrid methodology, some of the importantdefinitions about spherical fuzzy sets are explained in the fol-lowing subsection.

Preliminaries of spherical fuzzy sets

Intuitionistic and Pythagorean fuzzy sets consist of three pa-rameters as membership, nonmembership, and hesitancy. LetX is a fixed set. μep xð Þ : X↦ 0; 1½ � and vep xð Þ : X↦ 0; 1½ � definethe degree of membership and degree of nonmembership of

the element x ∈X to eP, respectively. Hesitancy degree (π) canbe calculated using Eq. 1 for intuitionistic fuzzy sets and usingEq. 2 for Pythagorean fuzzy sets.

πeI xð Þ ¼ 1−μeI xð Þ−veI xð Þ ð1Þ

πep xð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μep xð Þ2−vep xð Þ2

rð2Þ

Unlike the intuitionistic and Pythagorean fuzzy sets, thesum of membership, nonmembership, and hesitancy degreescan be smaller than 1 but each of them must be defined be-tween 0 and 1 in spherical fuzzy sets (Gündoǧdu andKahraman 2019).

Definition 1: A spherical fuzzy set is shown as eS in Eq. 3:

eS ≅ x; eP μes xð Þ; ves xð Þ;πes xð Þ� �

; x∈U� �

ð3Þ

whereU is a fixed universe used in function. μes xð Þ : X↦ 0; 1½ �,ves xð Þ : X↦ 0; 1½ � and πes xð Þ : X↦ 0; 1½ � defines the degree of

Table 1 Remarkable studies on different versions of fuzzy AHP integration

Year Author Fuzzy sets Method Application area

2012 Kutlu and Ekmekçioǧlu Traditional TOPSIS Failure modes and effects analysis

2009 Gumus Traditional TOPSIS Evaluation of transportation firms

2015 Turskis et al. Traditional WASPAS Site selection for construction

2017 Panchal et al. Traditional CODAS A decision on maintenance for fertilizer

2014 Cevik Onar et al. Type-2 TOPSIS Strategy selection

2016 Gul et al. Type-2 ELECTRE Performance evaluation

2016 Celik and Taskin Gumus Type-2 PROMETHEE Response ability evaluation

2019 Yilmaz et al. Type-2 DEA Performance evaluation

2017 Otay et al. Intuitionistic DEA Performance evaluation

2016 Büyüközkan and Güleryüz Intuitionistic TOPSIS Product development partner selection

2018 Liu and Zhang Intuitionistic ENTROPY Hotel selection

2018 Büyüközkan and Göçer Intuitionistic ARAS Supplier selection

2017 Wu et al. Intuitionistic VIKOR Site selection for plant

2015 Razieh and Ahmad Intuitionistic DEMATEL Manager selection

2019 Acar et al. Hesitant TOPSIS Performance evaluation

2020 Çolak et al. Hesitant TOPSIS Evaluation of blockchain technology

2020 Yildiz et al. Hesitant SAW Evaluation of employee experience

2020 Samanlioglu and Ayaǧ Hesitant VIKOR Project evaluation

2020 Sarucan and Söğüt Hesitant COPRAS Job evaluation

2018 Gul Pythagorean VIKOR Risk assessment for occupational safety

2020 Yucesan and Gul Pythagorean TOPSIS Service quality evaluation

2020 Song et al. Pythagorean TODIM Risk assessment for loan

2020 Yildiz et al. Pythagorean TOPSIS ATM site selection

2019 Kahraman et al. Neutrosophic DEA Performance evaluation

2019 Nabeeh et al. Neutrosophic TOPSIS Personnel selection

2020 Junaid et al. Neutrosophic TOPSIS Supply chain risk assessment

36111Environ Sci Pollut Res (2020) 27:36109–36120

membership, degree of nonmembership and degree of the

hesitancy of the element x ∈U to eS, respectively.0≤μes xð Þ2 þ ves xð Þ2 þ πes xð Þ2≤1; x∈U ð4Þ

Basic operations (addition and multiplication) of sphericalfuzzy numbers (Eqs. 5–6) are shown in definition 2 (KutluGündoğdu and Kahraman 2020).

Definition 2:The addition (Eq. 5) andmultiplication (Eq. 6) on

two spherical fuzzy numbers eα ¼ S μα; vα;παð Þ and eβ ¼ S

μβ; vβ;πβ

� �are given as follows:

eα⊕eβ ¼ eS ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ2eα þ μ2eβ−μ2eαμ2eβ

r; veαveβ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μ2eα� �

π2eβ þ 1−μ2eβ !

π2eα−π2eαπ2eβvuut0@ 1A

ð5Þ

eα⊗eβ ¼ eS μeαμeβ;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2eα þ v2eβ−v2eαv2eβ

r;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−v2eα� �

π2eβ þ 1−v2eβ !

π2eα−π2eαπ2eβvuut0@ 1A

ð6Þ

Multiplication by a scalar of spherical fuzzy numbers andpower of spherical fuzzy numbers are given in definition 3.

Definition 3:Multiplication by a positive scalar (λ) is given inEq. 7 and the positive power of eα is given in Eq. 8.

λeα ¼ eSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−μ2eα� �λ

s; vλeα;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μ2eα� �λ

− 1−μ2eα−π2eα� �λ

s0@ 1Að7Þ

eαλ¼ eS μλeα;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−v2eα� �λ

s;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−v2eα� �λ

− 1−v2eα−π2eα� �λ

s0@ 1Að8Þ

Extension of spherical fuzzy WASPAS with sphericalfuzzy AHP

The proposed spherical fuzzy AHP-integrated spherical fuzzyWASPAS methodology is composed of two main stages.Firstly the main and sub-criteria weights are determined byAHP using spherical fuzzy numbers. Then, these weights areused as criteria weights in WASPAS and the best alternativesare ranked from best to worst. The proposed integrated meth-odology steps can be seen in Fig. 1. The steps of the proposedintegrated methodology are detailed theoretically in the fol-lowing steps.

Step 1. Determine criteria and alternatives for a decision-making problem.

Step 2. Gain information from experts to establish pairwisecomparison matrices. The experts define their opin-ions using linguistic terms given in s 2 (Gündoǧduand Kahraman 2019).

Step 3. Construct spherical fuzzy pairwise comparison ma-trices using the linguistic terms among all thecriteria for two hierarchical levels of criteria.

M ¼1 ea12 ⋯ ea1nea21 1 ⋯ ea2n⋮ ⋮ ⋱ ⋮ean1 ean2 ⋯ 1

2666437775 ð9Þ

Let eaij is the pairwise comparison i and j.Step 4. Calculate score indices (SI) of each element of

pairwise comparison using Eq. 10 for havingmore importance (AMI, VHI, HI, SMI), usingEq. 11 for having less or equal importance(ALI, VLI, LI, SLI, EI).

SI ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi100 μ2eα−π2eα

� �2

− v2eα−π2eα� �2

" #

vuut ð10Þ

1

SI¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

100 μ2eα−π2eα� �2

− v2eα−π2eα� �2

" #

vuut ð11Þ

Step 5. Test the consistency of the constructed pairwisecomparison matrices using score indices. Use scoreindices calculated in step 4 to find the consistencyratio (CR) of a matrix as proposed by Saaty(1977)). Matrix consistency index (CI) is calculat-ed by Eq. 12

CI ¼ λmax−nn−1

ð12Þ

CR is calculated by Eq. 13:

CR ¼ CIRI

ð13Þ

λmax is the largest or principal eigenvalue of the A decisionmatrix of pairwise comparison. Random index (RI) dependson matrix order (n) and is calculated using the table proposedby Saaty (Saaty 1977). If the consistency ratio is calculated asless than 0.1, the relevant matrix is accepted as consistent andthe weight calculation step is started.

Step 6. Calculate the spherical fuzzy weights for each crite-rion using a spherical weighted arithmetical mean(WM) operator given in Eq. 14.

36112 Environ Sci Pollut Res (2020) 27:36109–36120

gWM eα1; eα2;…; eαn

�¼ eS ð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1−∏nj¼1 1−μ2eα j

!wvuut ;

∏nj¼1v

weα j

;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∏n

j¼1 1−μ2eα j

!λ

−∏nj¼1 1−μ2eα j

−π2eα j

!wvuut Þ

ð14Þ

where n is the number of criteria and w = 1/n.

Step 7. Defuzzify spherical fuzzy numbers in order to de-termine the importance levels of the criteria, usingEq. 15.

S gWM �

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi100 3μfWM

−πfWM

2

!2

−vfWM

2−πfWM

!224 35

vuuutð15Þ

Step 8. Normalize the defuzzified criteria weights using Eq.16.

wj ¼S gWM j

�∑n

i¼1S gWMij

� ð16Þ

Step 9. Construct spherical fuzzy decision matrix to evalu-ate alternatives according to specified criteria,

assigning linguistic terms shown in Table 2. eX ij

denotes the evaluation values of alternative i respectto criterion j.

Step 10. Calculate each element of the weighted decisionmatrix using Eq. 17.

exijw ¼ exijw j ¼ eSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−μ2exij !w j

vuut ; vw jexij ;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μ2exij !w j

− 1−μ2exij−π2exij !w j

vuut0@ 1Að17Þ

Step 11. Calculate the weighted sum model eQ1 �

for eachalternative by Eq. 18. Each addition term is calcu-lated using Eq. 19.

eQ1

i ¼ ∑mi¼1exijw ð18Þ

exi1w⊕exi2w ¼ eS ð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ2exi1w þ μ2exi2w−μ2exi1wμ2exi2w

r; vexi1wvexi2w;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1−μ2exi1w !

π2exi2w þ 1−μ2exi2w !

π2exi1w−π2exi1wπ2exi2wvuut Þ

ð19Þ

Step 12. Calculate each element of the decisionmatrix usingEq. 20.

exw j

ij ¼ eS μw jexij ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−v2exij !w j

vuut ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−v2exij

!w j

− 1−v2exij−π2exij !w j

vuut0@ 1Að20Þ

Step 13. Calculate the weighted product model eQ2 �

foreach alternative by Eq. 21. Each addition term iscalculated using Eq. 22.

eQ2

i ¼ ∏nj¼1exw j

ij ð21Þ

exw1

i1 ⊗exw2

i2 ¼ eS ðμexw1i1 μexw2i2 ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2exw1i1 þ v2exw2i2 −v2exw1i1 v2exw2i2

r;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−v2exw1i1

!π2exw2i2 þ 1−v2exw2i2

!π2exw1i1 −π2exw1i1 π2exw2i2

vuut Þð22Þ

Step 14. Specify threshold value to combine the weightedsum model and weighted product model.Calculate Eq. 23 and Eq. 24.

λeQ1

i ¼ eSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−μ2eQ1

i

!λvuut ; vλeQ1

i

;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μ2eQ1

i

!λ

− 1−μ2eQ1

i

−π2eQ1

i

!λvuut0@ 1A

ð23Þ

1−λð ÞeQ2

i ¼ eS ð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− 1−μ2eQ2

i

! 1−λð Þvuut ; v1−λeQ2

i

;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−μ2eQ2

i

! 1−λð Þ− 1−μ2eQ2

i

−π2eQ2

i

! 1−λð Þvuut Þ

ð24Þ

Step 15. Use Eq. 25 to calculate the relative significance ofalternatives.

eQi ¼ λeQ1

i þ 1−λð ÞeQ2

i ð25Þ

Step 16. Defuzzify spherical fuzzy numbers in order to de-termine the final scores of the alternatives usingEq. 15.

Step 17. Order alternatives according to the final score.Determine the highest final score as the bestalternative.

36113Environ Sci Pollut Res (2020) 27:36109–36120

The numerical application for İstanbul

The proposed methodology is applied to the petrol stationlocation selection problem. For this problem, thirteen candi-date locations in İstanbul, which are located on the Anatolianside of the city, are evaluated. As a location selection problem,the problem of taking over one of the candidate facilities iden-tified is addressed. Istanbul is located where Asia and Europecontinents connect. The city, where approximately 15 millionpeople live in, is very important for the country’s economy.The location of the petrol station in a city such as Istanbul,where crowds and vehicles are intense, is very important interms of financial perspective. In the application discussedhere, one of the candidate station shown in Fig. 2 is to be takenover.

The candidate locations are shown in Fig. 2. In this study,since the station is examined both before the installation (lo-cation selection) and after the installation (operation), the eval-uation is made over the existing operating stations. Thesestations that are currently working have fulfilled the legislativerequirements applied during the establishment stages.However, changes in legislation and standards may pose aproblem in their forward-looking investments, either to addnew products, to expand as places, etc. In addition, investorshave to think about the future financially, apart from legalrequirements. In this context, the potentials of candidate loca-tion should also be taken into consideration. For these reasons,it is most reasonable for the investor to choose the station thatcomplies with the current legislative requirements and is opento the changes for the future.

A two level hierarchy consists of four main and sixteensub-criteria is established to evaluate the criteria and deter-mine the best alternative to take over as a petrol station.These main and sub criteria are searched by a comprehensiveliterature review and the most appropriate ones are determinedby consulting with the experts. The experts are determined byconsidering their experiences in the related sectors. The mainand sub-criteria discussed in the study are given in Fig. 3.

In this study, the criteria for the petrol station location se-lection problem are considered and classified into four differ-ent main criteria as Financial, Environmental, Opportunities,and Supplier.

Financial factors play an important role in determiningthe location of the petrol station. Financial main criterionconsists of takeover, operation, and maintenance costs.Takeover Cost covers the cost of the station incurred whilethe station is being taken over, the cost of the opening of theworkplace and the transfer of the work permit, the unfore-seen old debts of the workplace, the cost of the consultancyfirm, and the feasibility cost. Maintenance Cost includesthe renewal and maintenance costs of the station taken over.Operation Cost consists of rent/land price, employee expenses,cost of electricity, water, etc.

Environmental main criterion must be taken into accountfor the decisions of corporate strategy. Population is the pop-ulation density in the district where the station is located.Proximity to the Airport and Bus Terminals means the prox-imity of the passengers’ gathering points. Proximity to theCenter refers to the distance of the petrol station to the districtcenter. Proximity to Highways refers to the distance from themain arteries of the city.

Opportunities are a critic for making an investment deci-sion; so it is taken into consideration in this study. IncomeLevel refers to the income level of the district where the petrolstation is located. Auxiliary Services cover automatic carwashing, lubrication, spare parts supply, cold/hot food andbeverage service, market, WC, etc. Facility Area refers tothe physical area of the petrol station. Accessibility refers tothe ease of transportation to the station by car. Lastly, Numberof Petrol Stations expresses the number of petrol stations inthese districts and their activities.

The last main criterion taken into consideration is theSupplier. It covers supplier related issues. The first one isBrand and it refers to the supplier distribution company.Promotion is the financial support of the supplier to the stationtaken over. Product Range refers to the product range of thesupplier. Supply Service refers to the logistics services of thedistributor company in product supply.

The importance weights of each criterion for the petrolstation location selection problem are obtained by the pro-posed methodology. Two experts from the TurkishEnvironment and Urban Ministry, one expert from aPrivate Energy Firm and two experts from non-governmental firms are employed to evaluate criteria.These experts work for petrol station operations. Face toface interviews are conducted with experts to get theirideas on criteria. The experts use the scale given inTable 2, to evaluate the criteria.

First, the consolidated pairwise comparisons of the maincriteria are structured by experts using linguistic variables.The main criteria pairwise comparisons can be seen inTable 3.

As a result of the abovementioned calculations given infrom step 1 to step 8, the weights of four main criteria aredetermined. The importance weights of the four main criteria,Financial, Environmental, Opportunities, and Supplier arecalculated as 0.314, 0.261, 0.190, and 0.235, respectively.The most significant main criterion for the handled problemis specified as the Financial with the importance of 0.314.Environmental and Supplier are also important main criteria.Opportunities is the least significant main criterion for thepetrol station location selection problem with a rate of 0.19according to the results.

Then, the pairwise comparisons of the sub criteria for eachof the main criteria are performed. The sub criteria local im-portance weights are also calculated. So, the final criteria

36114 Environ Sci Pollut Res (2020) 27:36109–36120

weights are determined. Table 4 gives the local and finalweights of sub-criteria.

If the sub-criteria are focused on, it can be seen that theTakeover Cost is the most important sub-criterion with thehighest importance rate of 0.128 It can be said that TakeoverCost has more impact on the whole system than the other subcriteria. Then, Operation Cost and Proximity to the CityCenter must be taken into consideration, with importancerates of 0.104 and 0.087, respectively. Also, the least

important sub-criterion is obtained as Facility Area with theimportance rate of 0.026.

The weights of the main and sub-criteria are calculated up tonow, and then, these values can be used for comparison of thealternatives. Therefore, steps 9–17 of the proposed method areoperated. The results of the weighted sum model and weightedproduct model of each alternative are given in Table 5.

The threshold value (λ) is taken as 0.5 in this study accord-ing to literature (Kaynak). The results of the proposed novel

Table 2 Definition and fuzzyscales of linguistic variables Linguistic variables Spherical fuzzy numbers Score index (SI)

μ v π

Absolutely low important (ALI) 0.1 0.9 0 1/9

Very low important (VLI) 0.2 0.8 0.1 1/7

Low important (LI) 0.3 0.7 0.2 1/5

Slightly low important (SLI) 0.4 0.6 0.3 1/3

Equal important (EI) 0.5 0.5 0.4 1

Slightly high important (SHI) 0.6 0.4 0.3 3

High important (HI) 0.7 0.3 0.2 5

Very high important (VHI) 0.8 0.2 0.1 7

Absolutely more important (AMI) 0.9 0.1 0 9

Fig. 1 The proposed methodology

36115Environ Sci Pollut Res (2020) 27:36109–36120

spherical fuzzy AHP-integrated spherical WASPAS method-ology are presented as scores and the final ranking of alterna-tives in Table 6.

As can be seen from Table 6, the best alternative isKadıköy with a score of 20.495. Şile is the worst optionto be an appropriate location for the petrol station.

Fig. 2 Locations of alternatives

Fuel Sta�on Site Selec�on

Financial Opportuni�esEnvironmental Supplier

Take

over

Cos

t

Ope

ra�o

n Co

st

Mai

nten

ance

Cos

t

Inco

me

Leve

l

Auxi

liary

Ser

vice

s

Faci

lity

Area

Acce

ssib

ility

Num

ber o

f Pet

rol

Sta�

ons

Popu

la�o

n

Prox

imity

to th

e Ce

nter

Prox

imity

to H

ighw

ays

Prox

imity

to th

e Ai

rpor

t an

d Bu

s Ter

min

als

Bran

d

Prom

o�on

Prod

uct R

ange

Supp

ly S

ervi

ce

Fig. 3 Main and sub-criteria for petrol station location selection problem

36116 Environ Sci Pollut Res (2020) 27:36109–36120

Pendik and Maltepe are also good alternatives to takeover.

Sensitivity analysis

A sensitivity analysis is conducted to show the reliability andapplicability of the proposed methodology. The proposedmethodology results are discussed in the sensitivity analysis.The sensitivity analysis is performed by a 0.1 increase in thevalue of the threshold number (λ), which changes from 0 to 1.It shows the robustness of the location selection decision. Thefinal appraisal scores of each alternative according to sensitiv-ity analysis are given in Table 7.

The sensitivity analysis shows that the changing value of thethreshold number (λ) can change the results as expected. Thereason for this may be that the alternatives have the differentweighted sum andweighted product values. As the final apprais-al scores change, the ranking of the alternatives changes forseveral different threshold values. The final rankings of the alter-natives according to sensitivity analysis are shown in Fig. 4.

By focusing on the results of sensitivity analysis, given inTable 7 and Fig. 4, it can be seen that the best alternative isnever changing. So, it can be said that Kadıköy is always thebest option to take over. Maltepe and Pendik are also betteralternatives among candidates. They are always in the topthree for each threshold value. The ranks of the last sevenalternatives are never changing also according to the sensitiv-ity analysis.

Conclusion and future directions

In this paper, the petrol station location selection problem istaken into account. To identify the main and sub-criteria for

Table 3 Pairwise comparison matrix for the main criteria

Financial Environmental Opportunities Supplier

Financial EI SMI HI SMI

Environmental SLI EI SMI SMI

Opportunities LI SLI EI SLI

Supplier SLI SLI SMI EI

Table 4 The local and final weights of sub-criteria

Main criteria Weight Sub-criteria Localweight

Finalweight

Financial 0.314 Takeover cost 0.409 0.128

Maintenance cost 0.261 0.082

Operation cost 0.331 0.104

Environmental 0.261 Population 0.316 0.083

Proximity to the airportand bus terminal

0.157 0.041

Proximity to city center 0.335 0.087

Proximity to highways 0.192 0.050

Opportunities 0.190 Income level 0.204 0.039

Auxiliary services 0.164 0.031

Facility area 0.135 0.026

Accessibility 0.274 0.052

Number of petrol stations 0.222 0.042

Supplier 0.235 Brand 0.250 0.059

Promotion 0.153 0.036

Product range 0.325 0.076

Supply service 0.272 0.064

Table 5 The results of the weighted sum model and weighted productmodel

Weighted sum model Weighted product model

μ v π μ v π

Ataşehir 0.526 0.562 0.201 0.488 0.607 0.232

Beykoz 0.382 0.709 0.222 0.305 0.772 0.207

Çekmeköy 0.429 0.658 0.224 0.387 0.698 0.227

Kadıköy 0.583 0.507 0.151 0.508 0.608 0.166

Kartal 0.509 0.577 0.212 0.481 0.610 0.236

Maltepe 0.543 0.546 0.154 0.489 0.618 0.161

Pendik 0.560 0.533 0.166 0.487 0.621 0.192

Sancaktepe 0.376 0.720 0.201 0.278 0.796 0.175

Sultanbeyli 0.334 0.748 0.226 0.282 0.788 0.205

Şile 0.305 0.798 0.161 0.165 0.884 0.110

Tuzla 0.428 0.665 0.244 0.363 0.720 0.252

Ümraniye 0.484 0.608 0.222 0.426 0.667 0.244

Üsküdar 0.528 0.565 0.152 0.443 0.667 0.156

Table 6 The results andthe final ranking ofalternatives

Rank Alternative Score

1 Kadıköy 20.495

2 Pendik 19.626

3 Maltepe 19.484

4 Ataşehir 18.786

5 Üsküdar 18.508

6 Kartal 18.319

7 Ümraniye 16.860

8 Çekmeköy 15.154

9 Tuzla 14.572

10 Beykoz 12.844

11 Sancaktepe 12.424

12 Sultanbeyli 11.371

13 Şile 9.210

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evaluation, the literature is reviewed and five experts fromdifferent companies are interviewed to determine the mostappropriate ones. After that, thirteen different alternative loca-tions are specified to takeover. Then, the novel spherical fuzzyAHP-integrated spherical WASPAS methodology is struc-tured; and the petrol station location selection problem is eval-uated with this methodology. In this study, a real application ispresented for İstanbul. Finally, a sensitivity analysis is per-formed to explain and analyze the proposed methodologyresults.

The contributions of this work can be summarized as fol-lows: (1) petrol station location selection problem is

considered as a multicriteria decision-making problem; (2)the most important factors to petrol station location selectionare identified and grouped; (3) these main criteria and theirsub criteria are evaluated by the proposed methodology togain importance weights of each criterion; (4) a real-life ap-plication in İstanbul is performed and presented to show theapplicability and reliability of the proposed methodology; (5)it is aimed that the proposed methodology can be used byorganizations to improve their location selection strategies;(6) to the best of our knowledge, this work includes the firstapplication of spherical fuzzy AHP-integrated spherical fuzzyWASPAS methodology.

Table 7 The final appraisal scores according to sensitivity analysis

Alternative Threshold value and final scores

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ataşehir 18.012 18.172 18.328 18.483 18.636 18.786 18.934 19.080 19.225 19.367 19.507

Beykoz 11.268 11.607 11.933 12.248 12.551 12.844 13.128 13.402 13.669 13.927 14.178

Çekmeköy 14.341 14.509 14.675 14.837 14.997 15.154 15.308 15.460 15.610 15.757 15.902

Kadıköy 19.119 19.414 19.698 19.973 20.239 20.495 20.743 20.984 21.216 21.441 21.660

Kartal 17.739 17.857 17.975 18.091 18.205 18.319 18.431 18.543 18.653 18.762 18.870

Maltepe 18.483 18.694 18.899 19.099 19.294 19.484 19.671 19.852 20.030 20.204 20.374

Pendik 18.208 18.510 18.803 19.086 19.360 19.626 19.883 20.133 20.375 20.611 20.839

Sancaktepe 10.366 10.821 11.252 11.661 12.051 12.424 12.781 13.124 13.454 13.771 14.077

Sultanbeyli 10.329 10.548 10.762 10.970 11.173 11.371 11.564 11.752 11.936 12.117 12.293

Şile 5.723 6.598 7.357 8.034 8.647 9.210 9.732 10.220 10.678 11.110 11.520

Tuzla 13.219 13.505 13.783 14.053 14.316 14.572 14.821 15.063 15.300 15.531 15.756

Ümraniye 15.667 15.917 16.161 16.400 16.632 16.860 17.082 17.299 17.511 17.718 17.921

Üsküdar 16.848 17.207 17.551 17.882 18.201 18.508 18.804 19.089 19.365 19.631 19.889

123456789

10111213

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rank

ing

Threshold Value

Ataşehir Beykoz Çekmeköy Kad köy Kartal Maltepe Pendik Sancaktepe Sultanbeyli Şile Tuzla Ümraniye Üsküdar

Fig. 4 The final rankings of alternatives according to sensitivity analysis

36118 Environ Sci Pollut Res (2020) 27:36109–36120

Different multicriteria decision-making methods or heuris-tics can be included in the methodology to ensure a morecomparative and integrated study as a future direction. Thenumber of experts consulted can be increased. The organiza-tions can be compared by using this work. Performance eval-uation of petrol stations may be performed.

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