key: cord-0821726-0rxpyy2c
authors: Ayyildiz, Ertugrul; Taskin, Alev
title: A novel spherical fuzzy AHP-VIKOR methodology to determine serving petrol station selection during COVID-19 lockdown: A pilot study for İstanbul
date: 2022-05-24
journal: Socioecon Plann Sci
DOI: 10.1016/j.seps.2022.101345
sha: e9e8f90c64ccd9ada5156bfa6dabc2c79a93271b
doc_id: 821726
cord_uid: 0rxpyy2c

COVID-19 pandemic has affected the entire world. During the Covid-19 pandemic, which is tried to be prevented by all countries of the world, regulations have been made to reduce the effect of the virus in sectors such as banking, tourism, and especially transportation. Social isolation is one of the most critical factors for people who have or are at risk of contracting COVID-19 disease. Many countries have developed different solutions to ensure social isolation. By applying lockdown for specific periods, preventing the movement of people will reduce the rate of transmission. However, some private and public institutions that have to serve during the lockdown period should be carefully determined. In this study, we aim to determine the petrol stations to serve during the COVID-19 lockdown, and this problem is handled as a multi-criteria decision-making problem. We extend the spherical fuzzy VlseKriterijumska Optimizacija IKompromisno Resenje (SF-VIKOR) method with the spherical fuzzy Analytic Hierarchy Process (SF-AHP). To show its applicability in complex decision-making problems, Istanbul is selected to perform a case study; thirteen petrol stations are evaluated as potential serving petrol station alternatives during the lockdown. Then, the novel SF-AHP integrated SF-VIKOR methodology is structured; the problem is solved with this methodology, and the best alternative is determined to serve in lockdown. Accessibility of the petrol station and Measures taken by station managers are determined to be essential for the effectiveness of the lockdown process. The neighborhood population and the station's proximity to hospitals are also critical inner factors to fight the pandemic. To test the methodology, Spherical Fuzzy the Weighted Aggregated Sum-Product Assessment (SF-WASPAS) is utilized. Public or private organizations can use the proposed methodology to improve their strategies and operations to prevent the spreading of COVID-19.

In December 2019, the pneumonia epidemic, first seen in Wuhan city of China, due to the newly defined SARS-CoV-2 factor, is defined as Coronavirus disease 2019 (COVID-19) [1] . The epidemic spreads rapidly, and on January 26, 2020, the existence of the virus was confirmed on all continents except Antarctica [2] . The first COVID-19 case in Turkey was detected on March 11, 2020. On the same date, the World Health Organization (WHO) announced this epidemic as a pandemic [3] . According to the reports published by WHO, there are more than seven million confirmed cases and more than four hundred thousand deaths in earlier June 2020 [4] . Studies for the treatment of such a large epidemic affecting 217 countries in the world are still ongoing.

COVID-19 is transmitted from person to person very quickly by droplet [5] - [7] . COVID-19 can be transmitted by the secretions of infected people caused by coughing and sneezing when they contact a healthy person's hands [8] . Also, COVID-19 is smeared from contaminated dry surfaces through hands, nose, eyes, or mouth mucous membranes [9] . For this reason, methods such as social isolation, use of personal protective equipment (mask, gloves, etc.), and protection of social J o u r n a l P r e -p r o o f managers of these institutions is important to provide these services properly and operate the institutions effectively. Public transport or private vehicles can be used for transportation. The fuel needs of public transit and private vehicles can only be provided by authorized petrol stations. In this context, the determination of the petrol stations to serve during lockdown is essential. Multiple factors should be taken into account when determining which stations to serve during the lockdown. In addition, the factors related to the spread of the outbreak must be taken into consideration while meeting the need for fuel. So the process of deciding on which station(s) to serve during lockdown should involve both quantitative and qualitative criteria. This is a classical type of decision-making problem. The decision-making problems usually include more than one criteria are called multi-criteria decision-making problems. To the best of our knowledge, there is no comprehensive study in the literature about the petrol station selection problem considering the pandemic conditions.

Upchurch et al. focus on the petrol station site selection problem. A capacitated location model is presented with some constraints related to vehicles' numbers [20] . Lim and Kuby present an algorithm-based solution methodology to select the most appropriate site for a petrol station that sells alternative fuels [21] . Sun et al. present a location model of a petrol station for network expansion strategy. Set covering method is used with a greedy algorithm to determine the size and location of a new petrol station considering existing petrol stations [22] . Aslani and Alesheikh present a GIS-based solution for the location selection of petrol stations, especially small stations.

They define the criteria and weighted criteria with fuzzy Analytical Hierarchy Process (AHP) methodology, and then GIS is used to determine the best alternative [23] . MirHassani and Ebrazi develop a set covering mathematical model to handle the location selection of petrol stations [24] .

Montoya et al. present a mixed-integer mathematical model for vehicle routing problems that J o u r n a l P r e -p r o o f consider the environmental risk to select the best petrol station location. A heuristic algorithm is used to solve this mathematical model [25] . Khahro and Memon search the most appropriate land with Geographic Information System (GIS) for building petrol station [26] . Ayyildiz and Gumus define the petrol station location selection criteria and propose a fuzzy multi-criteria decisionmaking approach. The alternatives are evaluated considering a real case study [27] .

As seen from the literature review, location selection of petrol stations is one of the topics handled in the academic literature. But, there is a very limited number of studies examining this problem as a multi-criteria decision-making problem. Also, to the best of our knowledge, there is no study for determining which petrol station(s) to serve during the lockdown, considering the pandemic conditions. Therefore, a comprehensive set of criteria is defined, and these criteria are weighted in this study. This study presents the most comprehensive criteria structure to determine which petrol station(s) to serve during lockdown which all the factors are included in terms of pandemic conditions. Further, this problem is solved in the spherical fuzzy environment to represent uncertainties and fuzziness in the decision-making process for the first time in the literature. To cope with this complex decision-making problem, spherical fuzzy VlseKriterijumska Optimizacija IKompromisno Resenje (VIKOR) is extended with AHP under a spherical fuzzy environment, and the Spherical Fuzzy AHP (SF-AHP) integrated spherical fuzzy VIKOR (SF-VIKOR) methodology is presented to the literature as a novel decision-making methodology.

Thanks to the proposed AHP and VIKOR combination under a spherical fuzzy environment, more detailed and comprehensive criteria set can be included in the evaluation process to make more accurate decisions in complex decision-making problems. These criteria can be grouped in a hierarchical structure and weighted more systematically. Thus, the opinions of decision-makers about the criteria can be integrated into the process more effectively. By using systematically J o u r n a l P r e -p r o o f weighted criteria in the VIKOR method, alternatives can be evaluated in more detail. In addition, with the proposed combination, the same experts can be consulted for criteria weighting and alternative evaluation, as well as different experts for criteria weighting and different experts for alternative evaluation.

In spherical fuzzy sets (SFS), decision-makers define a membership function on a spherical surface.

Thus, by generalizing other fuzzy set extensions, they can independently assign the parameters of the membership function to a larger domain [1] . SFS give decision-makers more freedom, and less information distortion is lead [2] . Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), have some limitations that make these sets insufficient to handle uncertainty in information and capture the complete information. Namely, there is no function to represent the degree of hesitancy by decision-makers [3] . Recently, the SFS are introduced to literature address this. SFS provide an effective way to determine ambiguity in information more impressively and represent decisionmakers' opinion better than the existing fuzzy sets [4] . SFS allow decision-makers to assign their hesitancy in the decision environment independently [1] . In this way, SFS enables the decisionmaking process to be more equivalent to human judgment, namely intelligent, so that SFS provide higher accuracy of determination of weight and evaluation of alternatives in the complex decisionmaking problems [5] . SFS can be considered as the integration of neutrosophic sets and PFS [6] .

Decision-makers express their degree of hesitancy like membership degree and non-membership degree in SFS [7] . Thus, SFS collect the advantages of other fuzzy sets in a unique theory [1] . SFS eliminate some disadvantages of neutrosophic sets and PFS.

AHP is one of the most used multi-criteria decision-making methodologies used to prioritize the criteria [28] . Researchers used AHP because of its utilization of a simple hierarchical structure to handle complex decision-making problems [29] . Ease of use is one of the advantages of using J o u r n a l P r e -p r o o f AHP. It provides the opportunity to evaluate qualitative and quantitative criteria together by including the priorities of the decision-maker in the decision-making problems. A decision problem allows both subjective and objective thoughts to be included in the decision process. AHP makes the decision-making process formal and systematic and ensures that the right decisions are made.

AHP method is an approach of MCDM, which analyzes the problem displayed in different levels of hierarchy [30] . It has a structure that simplifies complex problems [27] . AHP allows the decision-maker to measure the degree of consistency of their judgments. It is suitable for use in group decisions. The method uses the pairwise comparison of criteria. These comparisons allow decision-makers to determine the importance weight of criteria [31] . AHP enables decision-makers to make the right decision in complicated, complex, unorganized multi-criteria decision-making problems [32] . Determining the importance of criteria before solving the decision-making problem yields more reliable rankings of alternatives that reflect decision-makers' preferences more accurately [33] . For these reasons, we utilize AHP to determine the weights of criteria under a spherical fuzzy environment.

The VIKOR methodology focuses on ranking alternatives and selecting the best from a set of these alternatives. To determine the best option, many conflicting and non-commensurable criteria can be included [34] . The VIKOR methodology proposes an aggregating function that combines all considered criteria with their relative importance and a balance between the total satisfaction and individual regrets [35] . Aggregating function in VIKOR considers the distance from ideal solutions [36] . VIKOR enables the compromise solutions to resolve conflict [34] . Compromise means a mutual concession here [37] . This method helps decision-makers determine a compromise solution for the decision-making problem to reach a more accurate final decision [38] . For these reasons, SF-VIKOR is utilized to evaluate alternative stations to serve during the lockdown in this study.

In this study, the hierarchical criteria structure is constructed to define the criteria to determine the petrol station(s) to serve during the lockdown. Due to pandemic conditions, remote interviews with the expert group are conducted to take their opinions about criteria and alternatives. Then, the proposed methodology, which consists of SF-AHP and SF-VIKOR, is structured. The weights of each main and sub-criteria and specified alternative locations' evaluations are determined by the proposed hybrid decision-making methodology. The proposed methodology is applied to the Tuzla district of İstanbul to show its results and applicability.

This study is organized as follows: SFS are explained in Section 2. Related studies about SFS for multi-criteria decision-making are summarized in Section 3. The proposed novel methodology is presented in Section 4. Section 5 gives the real case study and sensitivity analysis of the proposed methodology. Comparative analysis is explained in Section 6. Finally, the results and future directions are given in the last section.

Fuzzy logic was first introduced to the literature by Zadeh [39] . The theory is suitable for subjective judgment and qualitative assessment in the evaluation processes of decision-making problems. The logic focuses on the rationality of uncertainty due to ambiguity. The linguistic approach is an effective method to solve uncertainty in information [40] . The multi-criteria decision-making problems may include more than one linguistic criteria. Different fuzzy sets can be used to define these linguistic criteria. IFS [41] , PFS [42] , type-2 fuzzy sets [43] , hesitant fuzzy sets [44] , and neutrosophic sets (NS) [45] are the most used sets in the literature [27] .

The degree of membership of an element to the set is defined with , and the degree of nonmembership to the set is defined with 1-in traditional fuzzy sets proposed by Zadeh. Therefore, the sum of the degrees of membership and non-membership equals 1. However, this situation is Atanassov has defined a third parameter called the degree of hesitancy to complete this sum to 1. The indeterminacy's degree is calculated by Eq. 2.3:

PFS were proposed by Yager [42] derived from IFS, which was originally proposed by Atanassov [41] . Unlike the IFS, the sum of membership and non-membership degrees can exceed 1, but the sum of their squares cannot be in PFS [46] , [47] as explained in Definition 2. defines the degree of non-membership of the element ∈ to P respectively and for every ∈ , it holds:

The indeterminacy ratio is obtained as in the following: 0 ≤ μ s (x) 2 + v s (x) 2 + π s (x) 2 ≤ 1; x ∈ U (2.8)

SFS are a new approach for multi-criteria decision-making process under a spherical fuzzy environment [48] . In SFS, functions are defined on a spherical surface to generalize fuzzy sets. So membership functions can be assigned in a larger domain [48] . SFS can be used to deal with the linguistic variables in the decision-making process. SFS are drawn the attention of many researchers and are later applied to many application areas. In this section, the multi-criteria decision-making literature related to the SFS is reviewed. Some remarkable studies based on SFS are given in Table 1 . Figure 1 shows the types of studies reviewed. Lastly, five papers are published in 2022. Different methodologies are used to solve decisionmaking problems. The methodologies used in reviewed papers can be seen in Figure 3 . there is no study that combines VIKOR and AHP under an interval-valued spherical fuzzy environment. So, this study proposes a novel approach involving SF-AHP integrated SF-VIKOR, which is developed for the first time to deal with complex decision-making problems. Besides, using a fuzzy multi-criteria decision-making approach for the first time for determining the serving station during a pandemic is one of the first innovations made in this paper. Therefore, the study contains novelties in terms of both the method adopted and the field of application.

The proposed fuzzy multi-criteria decision-making methodology that consists of SF-AHP integrated SF-VIKOR includes two main stages. In the first stage, the weights of each criteria level are determined by SF-AHP. Subsequently, SF-VIKOR is employed to rank alternatives using these weights. The proposed integrated methodology is given in Figure 4 , and it is detailed theoretically in the following steps.

J o u r n a l P r e -p r o o f 

Basic operations of spherical fuzzy numbers are shown as follows [63] .

The addition of two spherical fuzzy numbers α = S (μ α , v α , π α ) and β = S (μ β , v β , π β ) is:

Definition 5: The multiplication on two Spherical fuzzy numbers α = S (μ α , v α , π α ) and β = S (μ β , v β , π β ): 

Definition 7: The positive power ( > 0) of α is given:

Definition 8: Score value of α is calculated with Eq. 2.14.

Score (α ij ) = (2μ α − π α ) 2 − ( α − π α ) 2 (2.14)

Definition 9: Euclidian distance between two Spherical fuzzy numbers α = S (μ α , v α , π α ) and β = S (μ β , v β , π β ) is determined:

Step 1. The pairwise comparison matrix is constructed using information gained from anonymous experts. Linguistic terms (see Table 2 [48] ) are used to define opinions.

Step 2. The spherical fuzzy pairwise comparison matrix is established using the spherical fuzzy numbers.

(2. 16) where α ij = (μ α ij , v α ij , π α ij ) represents the pairwise comparison between i and j.

Step 3. Score indices (SI) are calculated for each comparison (α ij ). Random index (RI) depends on matrix order (n). RI is determined via the table [95] . The consistency ratio should be less than 0.1.

Step 5. The fuzzy weight for each criterion ( ) is calculated via a spherical weighted arithmetical mean. Step 6. Fuzzy numbers are defuzzified to determine the weight of each criterion.

Step 7. The weights of criteria are normalized to determine the final weights.

(2.23)

Step 8. All the above steps are repeated for each sub-criteria, and multiply local weights of the subcriteria with the weight of related main criteria.

Step 1. The decision matrix is established to evaluate alternatives according to criteria using linguistic terms using Table 2 . Then linguistic terms are converted to spherical fuzzy numbers. Let X ij is the spherical fuzzy evaluation values of alternative i with respect to criterion j.

Step 2. The Positive (X * ) and Negative Ideal (X − ) solutions are determined for each criterion based on the score values. Score value of X ij is calculated with Eq. 2.24. Step 3. and are calculated using Eq. 2.29 and Eq. 2.30 using criteria weights determined by spherical fuzzy AHP, respectively.

where represents the Euclidian distance as explained in Definition 9.

Step 4. is computed for each alternative: 

For this problem, thirteen candidate petrol stations in the Tuzla district of İstanbul are evaluated as a case study. As a serving petrol station selection problem during a lockdown, the problem of selecting one of the 13 alternative stations is addressed. İstanbul is located in the connection of Asia and Europe. The city, where more than 15 million people live, plays a key role in the economy of Turkey. Sixty percent of confirmed COVID-19 cases in Turkey are seen in İstanbul during the COVID-19 pandemic [97] . Also, more than fifty health institutions in the region treat many COVID-19 infected patients [98] . In this context, the services of public and private institutions in the region should continue during the lockdown. Therefore determining which fuel stations to serve during lockdown becomes more important.

J o u r n a l P r e -p r o o f

In the first stage of the proposed methodology, the main and sub-criteria are defined in order to determine the petrol stations to serve during a lockdown. A two-level hierarchical structure is constructed considering the criteria and their sub-criteria. Twenty-one different sub-criteria are taken into consideration to make a comprehensive analysis. These criteria are determined by literature review and consulting with anonymous experts. The criteria considered in this study are given in Figure 5 in the hierarchical structure. The last main criterion in this study is Population. It means the population density in the region where the petrol station is located. It includes total, infected, and risky populations. Risky population refers to people who have a chronic disease and are elder.

Firstly, an expert group is created to take opinions about criteria weights and alternative evaluation of petrol stations. The expert group consists of five experts, including three academicians and two managers. Academicians from different departments of universities and one manager from the public company, and one manager from the private company are consulted to take their opinions about a handled problem. All academicians have expertise in public health and related topics. The managers work on transportation operations for their institutions. Remote interviews are conducted with the expert group to get their ideas because of pandemic conditions. Experts are first asked to evaluate the main and sub-criteria using linguistic terms given in Table 2 . The aggregated pairwise comparisons of the five main criteria are evaluated by the expert group via linguistic terms as given in Table 3 . After all, matrices are determined as consistent, and the weight calculation process is repeated to determine the local weights of each sub-criterion. The local weights of each sub-criterion are multiplied with their related main criterion weight to find the final weight of the related subcriterion. So, the final criteria weights are determined as given in Table 9 . When Table 9 is analyzed, it is seen that the most important evaluation criterion is Neighborhood

Population. In other words, it is determined that the most important factor when choosing a petrol station to serve during lockdown is the number of people living close to the station. Besides, J o u r n a l P r e -p r o o f "Proximity to Hospital", "Vehicle Capacity", and "Risky Population in Neighborhood" are the factors that should be evaluated as a priority when choosing a station. The least important criterion is found to be "Brand". That is, the brand of gasoline and other products appear to be the factor that should be taken into consideration at the end of the list while determining the petrol station in the case of the lockdown.

After the criteria weights are calculated, the alternatives are evaluated according to the predetermined criteria. In determining alternatives, the districts in İstanbul are searched to apply the proposed methodology for the problem to show its applicability. At this point, Tuzla, a district of İstanbul, stands out with its proximity to the state and private sectors as it is a transportation hub.

Therefore, the proposed fuzzy methodology is applied to select which station to serve in lockdown among alternative stations in Tuzla. In the application discussed here, the candidate stations are shown in Figure 6 to serve during the lockdown. The same experts are employed to ask their opinions about the alternatives considering the criteria determined before by using the linguistic terms in Table 2 . Table 10 is created through the remote interviews, and the following evaluations are obtained. After receiving criterion-alternative evaluations from experts the best and the worst values for each criterion were determined as given in Table 11 . Therefore the ideal solutions are determined. , and were calculated using the weights obtained from SF-AHP and the ideal solutions are given in Table 11 . The threshold value ( ) is determined as 0.5 to combine the and the [49] .

, and values were calculated for each station and their rankings are determined with this way as given in Table 12 . If only one of them is selected, Alternative, and if two of them are selected, Alternative 7 and Alternative 4 should be determined as the best options together.

Alternative 7 is the best alternative to serve in lockdown according to the results of the proposed methodology. Alternative 7 stands out with its proximity to the city center, hospital, highways. It also has a bigger facility area and has more employees to serve customers. Alternative 4 is also a good option to serve in lockdown. Alternative 11 is the worst option to serve in lockdown for these reasons, which are its accessibility and measures.

In this subsection, a sensitivity analysis is performed to show the applicability and reliability of the The effect of threshold values on the order of the alternatives is measured by sensitivity analysis.

The reason for this is that each alternative has different values for both the weighted sum model and the weighted product model. As can be seen from Figure 7 , Alternative 7, which is the best alternative in the current situation, takes first place in all scenarios except 0.8 and 0.9, too. This means that the alternative, which is currently in the first place, is a good option the most cases to serve during a lockdown. The ranking of Alternative 8, which currently takes second place, is increased while the threshold value increases; so that it becomes the fifth-best alternative to serve during lockdown for 0.9. The reason for this may be that Alternative 8 has a relatively bad value for (the weighted maximum regret). As the threshold value increases, the effect of the increases. Alternative 4 is also a good option for all scenarios. As the threshold value increases, Alternative 13 achieves better rankings. This means Alternative 13 has a better result for the than the (the weighted total regret). J o u r n a l P r e -p r o o f

A comparative analysis is conducted to further validate the robustness and effectiveness of the proposed methodology to evaluate alternatives. SF-WASPAS methodology is employed to test the effectiveness of SF-VIKOR. The criteria weights determined by SF-AHP are used to evaluate alternatives for this purpose. The steps of SF-WASPAS are given below [27] :

Step 1. Weighted sum model (Q 1 ) is calculated for each alternative.

Step 2. Weighted product model (Q 2 )is calculated for each alternative.

Step 3. The threshold value (λ) is determined to combine Q 1 and Q 2 .

Step 4. The relative weights are calculated for each alternative. Step 5. Fuzzy numbers are defuzzified to determine the final scores of the alternatives.

Step 6. Alternatives are ranked according to the final score.

After receiving criterion-alternative evaluations from experts, the weighted sum model and the weighted product model are calculated. By taking into account the criteria weights obtained before, the weighted sum model and the weighted product model results are as in Table 11 . are ranked according to their final scores, as given in Table 12 . According to the results obtained, Alternative 7 has the highest score with 0.662. The best option is determined the same as the SF-VIKOR application. It is followed by Alternative 8 and Alternative 9 with scores of 0.597 and 0.507, respectively. The two alternatives with the lowest scores are determined as Alternative 11 and Alternative 6 with 0.044 and -0.047. The worst two options are the same as the proposed methodology again. Figure 8 demonstrates the proposed methodology results compared to those of the SF-WASPAS application. As can be seen in Figure   8 , the ranking order is similar to the result of the proposed methodology. As a result, the SF-VIKOR methodology not only provides a solution closer to the ideal but also provides a balance between the minimum individual regret for the "opponent" and maximum group utility of the "majority". In summary, the SF-VIKOR provides more valid and feasible results than other methods. Likewise, SF-VIKOR methodology is easier to apply decision-making problems, and it has less complexity. Therefore it provides a faster decision in complex decision-making problems.

The COVID-19 pandemic, which spread almost all over the world in a very short time with the effect of increasing human mobility with the increase in international trade and interaction, has progressed much faster than other epidemics experienced by human beings. It is not expected for J o u r n a l P r e -p r o o f countries to be fully prepared for a pandemic that spreads so rapidly and threatens human life.

Therefore, the fight of countries against the pandemic depends on their existing infrastructure and the structure of their populations. For this reason, countries have sometimes implemented lockdowns. In order to provide basic needs during these lockdown times, some institutions need to continue their operations. In this context, determining which of the petrol stations, which are important stakeholders for transportation, will remain open during a lockdown has become a problem to be solved for city planners.

In this paper, the determination of the petrol stations to serve during the COVID-19 lockdown is taken into account and handled as a multi-criteria decision-making problem. Literature review and opinions from experts are used to identify the main and sub-criteria. Then, an expert group that includes both academicians from different departments of universities and managers from public and private sectors is created to take opinions about criteria weights and alternative evaluation of petrol stations. İstanbul is selected to perform a case study; thirteen petrol stations are evaluated as alternatives. Then, the SF-AHP integrated SF-VIKOR methodology is structured; the problem is solved by this methodology, and the best alternative is determined to serve during a lockdown. A sensitivity analysis is performed to explain and analyze the proposed methodology results. Finally, the results are compared with SF-WASPAS.

This study considers five main criteria as Accessibility, Facility Area, Products, Measures, and

Population. According to the results, managers and city planners should pay special attention to Accessibility and Measures. The accessibility of the petrol station is important in the context of meeting basic needs during the lockdown process. In this way, the time spent on the road will decrease, and the probability of people getting infected by contacting fewer people will decrease.

Petrol stations, which are located close to areas where people are concentrated even during J o u r n a l P r e -p r o o f lockdown times, are effective in meeting demand. In addition, in these periods when ambulances work intensively, it is a necessity to determine the service stations close to the hospitals for effective management of the process. Ensuring the transportation of personnel working in hospitals, public and private institutions serving during the lockdown to their workplaces has also gained importance during the pandemic process.

In terms of Measures, by placing warning and informative posters and brochures at the stations, it is necessary for the customers to get service and meet their needs by contacting minimum people.

In addition, by using more modern payment methods, such as contactless payment, the use of cash, which people come into contact with frequently and which is likely to be contaminated, should be minimized. This study also suggests the capacity of stations should be increased, and the number of employees should be decreased.

The contributions of the paper to the literature and application can be specified as follows: (1) Nevertheless, this study carries certain limitations. First, the finding may be subject to a limited number of evaluation criteria with a hierarchal structure. One future study could extend the J o u r n a l P r e -p r o o f evaluation criteria with different aspects (i.e., financial, social) and inner factors of them. Second, consulted expert group in the application a potential limitation of the study. Reaching and consulting experts' opinions were challenging because of the pandemic. Expert opinions were taken through remote interviews instead of face-to-face interviews. Therefore the number of consulted experts can be increased. Third, the study is conducted in Istanbul, Turkey, which may not be generalized to other countries. The study can be modified and improved for other countries.

This study shows that multi-criteria decision-making is applicable for determining petrol stations to serve in lockdown, in part due to the numerous conflicting decision criteria present and the ability of multi-criteria decision-making methodologies to cope with the multidimensionality of the problem. However, frequently, different multi-criteria decision-making methods can yield different results when used to the same complex decision-making problem. Therefore, we examined the application of one of the widely applied methodologies, namely WASPAS, for the handled problem. The results show that the best alternative is valid for comparative analysis. As a future direction, Different multi-criteria decision-making methods or heuristics can be included and evaluated to identify similarities and differences in the different methods and the obtained results, and also consider their applicability in the handled problem. Integrated multi-criteria decision-making methodologies can improve the precision of determining petrol stations to serve in lockdown. Finally, different optimization and decision-making methods can be utilized to achieve different purposes, such as sorting, ranking, clustering, classification, along with determining the best alternative and the importance levels of criteria.

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Spherical fuzzy sets and decision-making applications

An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China

A Literature Review on Fuzzy FMEA and an Application on Infant Car Seat Design Using Spherical Fuzzy Sets

Spherical fuzzy VIKOR method and its application to waste management

A spherical fuzzy extension of MULTIMOORA method

AS/RS technology selection using spherical fuzzy TOPSIS and neutrosophic TOPSIS

Spherical fuzzy analytic hierarchy process (AHP) and its application to industrial robot selection

Advanced Fuzzy Sets and Multicriteria Decision-making on Product Development

A novel spherical fuzzy analytic hierarchy process and its renewable energy application

A novel fuzzy multi-criteria decision-making methodology based upon the spherical fuzzy sets with a real case study

A novel approach integrating AHP and TOPSIS under spherical fuzzy sets for advanced manufacturing system selection

Emergency decision support modeling for COVID-19 based on spherical fuzzy information

A novel entropy proposition for spherical fuzzy sets and its application in multiple attribute decision-making

Hospital location selection using spherical fuzzy TOPSIS

A spherical fuzzy TODIM approach for green occupational health and safety equipment supplier selection

A dynamic pricing model for location based systems by using spherical fuzzy AHP scoring

A modified failure modes and effects analysis using intervalvalued spherical fuzzy extension of TOPSIS method: case study in a marble manufacturing facility

Hospital Performance Assessment Using Interval-Valued Spherical Fuzzy Analytic Hierarchy Process

Hospital Preparedness Assessment against COVID-19 Pandemic: A Case Study in Turkish Tertiary Healthcare Services

Optimal Site Selection of Electric Vehicle Charging Station by Using Spherical Fuzzy TOPSIS Method

Evaluating Sustainable Vehicle Technologies for Freight Transportation Using Spherical Fuzzy AHP and TOPSIS

Spherical Fuzzy VIKOR with SWAM and SWGM Operators for MCDM

Multi-criteria Oil Station Location Evaluation Using Spherical AHP&WASPAS: A Real-Life Case Study

Prioritizing Manufacturing Challenges of a Contract Manufacturing Company for Personal Auto by

Interval-Valued Spherical Fuzzy MULTIMOORA Method and Its Application to

An integrated spherical fuzzy AHP multi-criteria method for COVID-19 crisis management in regarding lean six sigma

Using Spherical Fuzzy AHP Based Approach for Prioritization of Criteria Affecting Sustainable Supplier Selection

A Framework for Selection of the Best Food Waste Management Alternative by a Spherical Fuzzy AHP Based Approach

Evaluation of autonomous vehicle driving systems for risk assessment based on three-dimensional uncertain linguistic variables

Occupational health and safety risk assessment using an integrated TODIM-PROMETHEE model under linguistic spherical fuzzy environment

A hybrid spherical fuzzy MCDM approach to prioritize governmental intervention strategies against the COVID-19 pandemic: A case study from Vietnam

Process mining technology selection with spherical fuzzy AHP and sensitivity analysis

Prioritization of laminate flooring selection criteria from experts' perspectives: a spherical fuzzy AHP-based model

Spherical Fuzzy CRITIC Method: Prioritizing Supplier Selection Criteria

Spherical Fuzzy EXPROM Method: Wastewater Treatment Technology Selection Application

Spherical Fuzzy REGIME Method Waste Disposal Location Selection

A scaling method for priorities in hierarchical structures

Multi-criteria analysis of alternative-fuel buses for public transportation

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