Hesitant fuzzy linguistic TOPSIS method for the electric vehicles’ charging stations location selection problem and an application for Istanbul

1 Introduction

The transportation sector is found as one of the principal sources of greenhouse gas emissions in cities with a 40% share. In Kyoto Protocol, this sector is identified as one of the target sectors of greenhouse gas emission reduction efforts [1]. The negative environmental impacts of fossil-fuel vehicles may be the most crucial reason behind the need for alternative energy vehicles. However, there are other socio-economic reasons like as increasing oil prices and the need for energy alternatives to secure national energy requirements for the countries [2]. To satisfy this requirement and overcome the problems, electric vehicles have taken place as an alternative solution in recent years. It is observed that with the usage of Electric Vehicles (EVs) by commercial businesses and public users, more energy-efficient and environment-friendly transportation systems can be achieved [3].

Comparing the fossil-fuel vehicles, some of the advantages of EVs can be summarized as follows [4–7]. The cost of charging EVs is very low, and they are energy efficient and noiseless. When considering the CO₂ emission levels, they are very environment-friendly vehicles. However, there are also some crucial disadvantages that decrease the demand for EVs. Although some improvements are made in recent years, they have short driving ranges [7]. In addition, long charging times for slow charging stations may be an obstacle. Moreover, if the number of charging stations is not enough, and their locations are not selected conveniently, it may be the most critical disadvantage for the usage of EVs. As Kong et al. [8] state, if charging stations of EVs are not properly deployed, some adverse effects on the condition of traffic, drivers, power grid systems, and employees of charging stations can be observed. Also, the life cycle of charging stations depends on their locations. Operational efficiency and customer satisfaction degree on the quality of service can also be improved by finding proper locations for EVs’ charging stations [9].

EVs’ charging station types depend on the EVs types. Considering the fuel consumption technology, there are three EVs types [6]: hybrid electric vehicles, plug-in electric vehicles, and battery electric vehicles. Related to three EV types, charging types can be classified as [7]: conductive charging, inductive charging, and battery replacement. Conductive charging requires plug-in electricity and cable connection. Inductive charging can be done via electromagnetic transmission. In the battery replacement method, the batteries, which are in the same dimensions and standards, can be replaced with the discharged batteries. As Erbas et al. [7] state, cheaper and more efficient version is the conductive charging for the users and the industry. For the conductive charging (it can also be named as plug-in charging), as Bai et al. [10] explain, slow, medium, and fast charging options are applicable considering the power levels. Level 1 and level 2 charging are considered as low power charging options [11] and have long charging times. Hence, waiting times for the EV drivers maybe 2–8 hours [10]. Level 3 has a high-power charging capacity and provides a fast charging opportunity [11]. Battery replacement can be done very quickly.

Location types of charging stations can be parking-lot-based, gas-station based, and random-based [10]. Shopping malls and residential areas can be used as charging station locations, and this type of location is called parking-lot-based charging. EV users tend to stay relatively long times in these kinds of areas, and relatively slow charging times can be tolerable by them [10]. In this paper, parking-lot based charging location alternatives are evaluated for Istanbul. Considering its high population density, the usage of EVs is still not very widespread. However, it has great potential if proper infrastructure is provided for EVs. As explained previously, the most crucial factor may be the availability and the locations of the charging stations. In Istanbul, there is a large number of shopping malls, and they are spread to almost all districts of it. Considering their locations, some parts of their parking-lots may provide a great opportunity to serve as charging stations of EVs. Hence, in this study, 39 shopping-malls are considered as alternatives for EVs charging station locations and ranked by using an extended version of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to find the best locations for installing charging stations. To handle the uncertainty inherent to the evaluation process, probabilistic linguistic terms sets are used for evaluating the fuzzy type criteria within the proposed methodology. To the best of author’s knowledge, this is the first study utilizing extended TOPSIS for selecting the locations of EVs charging stations. Additionally, crisp and fuzzy type criteria are identified and processed simultaneously within the proposed methodology. Moreover, a real case is provided in Istanbul with a detailed representation of methodology steps.

The rest of this paper is organized as follows. In the next section, EVs charging station location selection problem’s literature is presented. In the third section, the basics of the used methodology are given; in the fourth section, an application from Istanbul, Turkey, is presented. Finally, concluding remarks are given in the last section.

2 Literature review

EVs’ charging station location selection literature is an emerging literature with an increased number of papers published in recent years. Like the other location selection applications, in this application area, studies can be classified into three groups. In the first group, mathematical models are presented, and exact solution approaches or heuristics/meta-heuristics are utilized as solution tools. In the second group, multi-criteria decision-making (MCDM) techniques are utilized to evaluate or rank alternative locations. Finally, in the third group, integrated MCDM-mathematical programming approaches are presented.

When the mathematical models established to find proper locations for EVs charging stations are considered, it is seen that almost half of the literature consists of these kinds of studies. One of the initial studies from this group was prepared by Zhu et al. [6]. They proposed a location model for charging stations. In this model, charging station locations and the number of the chargers to be established in each station was tried to be determined while minimizing the total cost. A method based on Genetic algorithm (GA) was used to solve the model. Additionally, numerical examples were given from Beijing, China. Another study was prepared by He et al. [12]. They proposed a bi-level programming model to find the locations for EVs charging stations. In their model, they considered the EVs’ driving range. In the upper level of their model, path flows of charging stations were tried to be maximized, and in the lower level, user equilibrium of route preferences were considered with EVs driving range constraint. In 2019, four studies were published for this literature. Zhang et al. [13] proposed a location model that considered the service capacity of potential charging stations to decrease the unmet demand risk. Also, they defined user anxiety as the fear of running out power while trying to reach the charging station and considered this factor in their model. They used whale optimization algorithm, which is a meta-heuristic to find a deployment structure for EVs charging stations. Liu et al. [14] presented a location model on public charging stations for EVs, which aimed to minimize CO₂ emissions. They applied the model for Chengdu, China taxi trip data, and used a particle-swarm meta-heuristics based optimization approach with a data-driven structure. Bai et al. [10] investigated the EVs charging station location selection problem for a city in which there was a low number of EVs. They divided the city into the segments and forecasted potential charging demand based on GPS trajectory data from the current vehicles data. Cost minimization and service quality maximization objectives were considered in a mixed-integer model. Non-dominated sorting genetic algorithm (NSGA-II) and neighborhood search heuristic were used as solution methodologies. The problem was applied for Shenzhen, China case. Kong et al. [8] prepared a paper on the location planning problem of fast charging stations of EVs. Operators, drivers, vehicles, traffic condition, and power grid dimensions were considered together with dynamic real-time data input. A simulation platform for planning was introduced, and Beijing, China data was used for the application. Sun et al. [4] proposed a location model for EVs charging stations. Urban residents’ travel behaviors were also taken into account in that study. Short distance and long distance travel demands were considered for different requirements of the residents. Slow charging and fast charging facilities were considered in the model for these different travel behaviors. An application from a city of China was presented.

When the studies which use MCDM techniques for EVs charging station location selection problems are considered, one of the initial studies was prepared by Li and Chang [15]. They introduced three different models related to functional areas and service windows for future investment plans of charging stations and applied the Analytic Hierarchy Process (AHP) for their evaluation process. In 2015, Guo and Zhao [16] applied a fuzzy TOPSIS methodology for charging station location problem and presented an application from Beijing, China. While selecting their criteria, a sustainability perspective was followed, and environmental, economic, and social criteria were considered. In 2017, Wu et al. [17] proposed a EVs charge station selection methodology for residential areas with intuitionistic triangular fuzzy numbers. A fuzzy VIKOR approach was utilized, and an application for Beijing, China was presented. They considered the uncertainty and hesitation of the decision environment. Xu et al. [11] proposed an interval type-2 fuzzy numbers based approach for EVs charging station locations and applied their methodology for Tianfu New district of China. Erbas et al. [7] proposed an MCDM method based on Geographic Information System (GIS) to find proper locations for charging stations in Ankara, Turkey. Fuzzy analytic hierarchy approach (FAHP) and TOPSIS methods were used for the evaluation process. Ju et al. [18] proposed a methodology for EVs charging station location selection problem via fuzzy picture environment AHP. Then, grey relational projection (GRP) was used for the evaluation of EVs. Also, an application for Beijing was presented. Hosseini and Sarder [9] prepared a study on the location of fast charging stations. They applied Bayesian Networks for their analyses and considered qualitative and quantitative factors from a sustainability perspective. They applied their approach to Iran case. Dascioglu et al. [19] applied an extended TOPSIS methodology for the charging station location selection problem of EVs for Istanbul. Finally, Karaşan et al. [20] proposed an MCDM method for the location selection problem of electric vehicles charge stations. They applied an integrated DEMATEL, AHP, TOPSIS methodology based on intuitionistic fuzzy sets and presented a case study for Istanbul.

In the third group, including the integrated MCDM techniques and mathematical programming approaches, three studies were found. Genevois and Kocaman [21] prepared a study for EVs charging station locations selection problem for Atasehir and Kadikoy districts of Istanbul. They evaluated the alternatives by using AHP, and obtained weights were used as an input for a mathematical model that was developed to find the number of charging stations to be installed. This model tried to maximize user utility. Ren et al. [5] proposed a location model that aimed to minimize total social cost. The model was solved by using a genetic algorithm approach to find the location and number of charging stations. They also used the grey decision-making technique for evaluation of EVs charging stations and considered factors like land cost, construction cost, road traffic flow, state of transmission of electricity, and the surrounding environment. Csiszar et al. [22] proposed a two-level methodology for EVs charging stations. Territory segments were evaluated by using a weighted multi-criteria method, and a hexagon-based approach and a greedy heuristic were applied to allocate the charging stations. They focused on intra-city demand and presented an application from Hungary.

As can be seen in the abovementioned literature, for the first group of studies, single objective, deterministic models are the most used models, and as solution approaches, metaheuristics are the most used ones. For the second category, within MCDM techniques, AHP and TOPSIS are the most used techniques. Some of these studies considered uncertainty inherent to this problem area and used some type of fuzzy numbers with their techniques. Classic fuzzy numbers, picture fuzzy numbers, and type-2 fuzzy numbers are used for the evaluation process. Also, considering all the groups of papers, in most of the studies, the cities from China, especially the city of Beijing, is considered as the application area.

Considering the literature and comments for EVs charging station location selection problem, the main contributions of this paper to the literature can be summarized as follows.

In Turkey, the usage of EVs is not prevalent. One of the main reasons for this may be the user anxiety related to the locations of charging stations. Considering the related literature, there exists a requirement for the studies for different cities for proper deployment of EVs charging stations. However, only three studies by Erbas et al.[7], Karaşan et al. [20], and Genevois and Kocaman [21] are found related. Erbas et al. [7] applied their methodology for the Ankara case, and Genevois and Kocaman [21] investigated only Kadıköy and Ataşehir districts of Istanbul. Karaşan et al. [20] evaluated nine alternatives from Asia and Europe sides of Turkey. They considered six shopping malls and three governmental facilities as alternatives. Although the considered case study is same with this study, the number of alternative locations varies.

As a result of the literature review part, this study contributes to the literature by being the first study which considers entire Istanbul as a case with a larger number of alternatives which scattered to the entire Istanbul. And also, alternatives are ranked not only for Istanbul, but also for different regions of Istanbul. Additionally, different from the existing studies about the electric charging station location problem, another main contribution of this study to the literature is about the methodology applied. Complexity and vagueness inherent to real-life problems result in hesitation for the decision-makers. With hesitation, taking the decision-makers’ opinions becomes more difficult. Extended versions of the fuzzy sets may provide a solution for this difficulty. However, for some situations, choosing one linguistic term set cannot be possible. In this study, the hesitation of decision-makers is examined via using probabilistic linguistic term sets within TOPSIS, which is detailed in the methodology part. Moreover, different from the existing studies, the criteria are firstly classified as crisp and fuzzy. Then, TOPSIS and extended TOPSIS are performed together in the same methodology to produce a combined final list of rankings.

3 Methodology

In daily life, people can more easily interpret and evaluate information in the form of linguistic expressions rather than exact, deterministic expressions. Lin et al. [23] stated in their study that decision-makers are required to provide their opinions about a criterion or an alternative with crisp data in the initial stages of decision-making problems. On the other hand, precise numbers are not a good way of presenting the uncertainty of human thinking; thus, evaluations are not presenting the complexity and the uncertainty of real life problems. In this regard, the fuzzy set theory is applied in different disciplines such as decision-making, engineering, mathematics problems, etc. [24-28]. However, fuzzy logic and its extended forms are vital, especially in decision-making problems.

The fuzzy set theory was first put forward by the Zadeh in 1965 [29]. In this way, instead of precise definitions in the classical set theory, vagueness can be considered to model the uncertain environments [30], therefore, many applications in different directions have been made and used frequently in the literature. Over time, the scope of the theory has been expanded and used in the analysis of processes that have different data systems. In basic fuzzy sets, which are also called as “Type-I Fuzzy Sets”, the membership function value equals a certain value in the range [0,1]. A membership function for a fuzzy set A, which is defined as a subset of universal set E, is represented by μ _A  (x) : E → [0, 1]. In this equation, μ _A  (x) represents the membership degree to set A. Thus, fuzzy set A is shown as A ={ μ _A  (x) , x }.

On the other hand, people in real-life applications are generally hesitant to provide their preferences, in other words, it may be hard to define a preference level for them. This uncertainty is not considered in the classical fuzzy set theory.

Intuitionistic fuzzy sets can be considered as an extended version of the fuzzy set theory and it models imperfect knowledge in a better way [31] and also called as “Type-II Fuzzy Sets”. While membership functions are defined in Type-I fuzzy set as membership and non-membership functions, the situation of hesitation is also taken into consideration in the Type-II fuzzy set theory. In many complex decision-making problems, the information provided by the decision-maker is insufficient and uncertain due to reasons such as time pressure, information inefficiency, or the ability of the decision-maker to have limited attention and assessment. For this reason, in many publications, it is mentioned that intuitionistic fuzzy sets are useful solution tools to describe uncertain decision-making information fairly well.

Intuitionistic fuzzy sets are generally defined as A = 〈 (x, μ_A (x) , v_A (x)) : x ∈ X〉 where μ_A (x) : X →  [0, 1] indicates membership and v_A (x) : X →  [0, 1] indicates non-membership function. These functions have a property of 0 ≤ μ_A (x) + v_A (x) ≤ 1. Therefore, hesitation is defined as П_A (x) = 1 - μ_A (x) - v_A (x). Although these sets are good in the analysis of hesitation, each choice is basically represented as a single point within the set. On the other hand, the data may be in a structure that cannot be expressed in a single point in terms of uncertainty or complexity and should be regarded as a range, rather than a single point. For this reason, Atanassov [32] proposed to expand the intuitionistic fuzzy set theory and developed interval-valued intuitionistic fuzzy set (IVIFs) theory.

IVIFs are generally defined as A ˜ = ( x , μ A ˜ ( x ) , v A ˜ ( x ) ) : x ∈ X , where IV [0, 1] represents the closed subsets, and μ A ˜ ( x ) : X → IV [ 0 , 1 ] indicates membership function and v A ˜ ( x ) : X → IV [ 0 , 1 ] indicates non-membership function. In an interval form, membership function can be expressed as μ A ˜ ( x ) = [ μ A L ˜ ( x ) , μ A U ˜ ( x ) ] , and non-membership function can be expressed as v A ˜ ( x ) = [ v A L ˜ ( x ) , v A U ˜ ( x ) ] . In this case, general function is, A ˜ = ( x , [ μ A L ˜ ( x ) , μ A U ˜ ( x ) ] , [ v A L ˜ ( x ) , v A U ˜ ( x ) ] ) : x ∈ X and have a property of 0 ≤ μ A U ˜ ( x ) + v A ˆ U ( x ) ≤ 1 .

Although extended versions of fuzzy sets generally provide a better solution for determining the opinions of decision-makers, still choosing one linguistic term set cannot be possible for some situations. In other terms, decision-makers mostly hesitate to choose the linguistic term sets for their assessments. Rodriguez et al. [33] stated that decision-makers could not easily provide their opinions generally because of the vagueness of the terms sets. The underlying reason for this problem is the consideration of several terms and approaches at the same time.

In 2014, Beg and Rashid [34] proposed an extended TOPSIS to overcome the problem, and they used hesitant fuzzy linguistic term sets (HFLTS). In 2016, Pang et al. [35] examined current studies about HFLTS. The study revealed that all possible values presented by decision-makers have equal importance in past studies, although it doesn’t reflect the real-life conditions. For that reason, Pang et al. [35] extended the approach for linguistic term sets and suggested probabilistic linguistic term sets (PLTS) to provide different importance degrees by considering probability. Let S = {S₀, S₁, …, S _τ } be a linguistic term set, then PLTS can be defined as in Equation 1;

L ( p ) = { L ( k ) , ( p ( k ) ) | L ( k ) ∈ S , p ( k ) ≥ 0 , k = 1 , 2 , … , # L ( p ) , ∑ k = 1 # L ( p ) p ( k ) ≤ 1 }(1)

Equation 1, L^(k) (p^(k)) represents the linguistic term, where L^(k) is associated with the probability p^(k), and # L (p) is the number of different linguistic term sets in L (p) [35]. An ordered PLTS depends on the subscript (r^(k)) of linguistic term L^(k) and can be achieved when the r^(k)p^(k) values are arranged in the descending order.

Basic operations of PLTS can only be applied after normalization, which can be done by ignoring probabilistic information or by normalizing the cardinality. In the study conducted by Pang et al. [35] both approaches for normalization are analyzed, and basic formulations are developed. Let assume L₁ (p) and L₂ (p) be any two PLTS. The normalization is given as in Equations 2 and 3;

If ∑ k = 1 # L ( p ) p i ( k ) < 1 then apply p ̇ ( k ) = p ( k ) ∑ k = 1 # L ( p ) p ( k ) for all k = 1 , 2 , . . , # L ( p ) and calculate L ̇ i ( p ) for i = 1 , 2 .(2)

If # L 1 ( p ) ≠ # L 2 ( p ) , then add elements to the smaller number of elements set .(3)

Real-life case studies generally consist of several decision-makers, therefore aggregation of the decision-makers’ thoughts is a vital step for every decision-making problem. In the literature, there are studies focused on the generation of aggregation operators like as presented in [35–39]. Let L i ( k ) and p i ( k ) represent the k^th linguistic term and its probability respectively, thus probabilistic linguistic averaging (PLA) operator and probabilistic weighted averaging (PLWA) operator are calculated as in Equations 4 and 5;

PLA ( L 1 ( p ) , L 2 ( p ) , … , L i ( p ) ) = 1 n ( L 1 ( p ) ⊕ L 2 ( p ) ⊕ … ⊕ L n ( p ) )(4) PLWA ( L 1 ( p ) , L 2 ( p ) , … , L i ( p ) ) = ( w 1 L 1 ( p ) ⊕ w 2 L 2 ( p ) ⊕ … ⊕ w n L n ( p ) )(5) where w = (w₁, w₁, …, w₁)  ^T and ∑ i = 1 n w i = 1 .

PLTS are started to be used widely in recent years, and hesitation of membership and non-membership functions are also included in more extended forms. Probabilistic uncertain linguistic terms sets are used by Lin et al. [36], and in the study, they integrated these sets with TOPSIS methodology. In another study conducted by Malik et al. [39], the uncertainty of probabilistic linguistic sets is also examined. In this study, these sets are used in a multi-criteria decision-making problem.

In this study, probabilistic linguistic terms sets and procedure that are defined by Pang et al. [35] are chosen to be used, and steps of the extended TOPSIS model are presented in Fig. 1. Moreover, the steps of TOPSIS are not provided in this study and can be seen in Lai et al. [40].

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Fig. 1

Steps of the probabilistic linguistic TOPSIS (Adapted from Pang et al. [35]).

In real-life problems, criteria selection is one of the most important steps in all MCDM problems. It is a well-known fact that characteristics of criteria can change such as objective and subjective, therefore, different evaluation scales in crisp or fuzzy structures are needed to be used. In this study, location selection problem of plug-in electric vehicles charging stations is examined in which different criteria types are used. Steps of the implemented methodology are presented in Fig. 2.

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Fig. 2

The steps of the proposed methodology.

The proposed methodology starts with the determination of the problem and alternatives with expert views. Afterwards, evaluation criteria are selected, and structures of these criteria are determined whether they are objective or subjective. In step 3, selected criteria are weighted, and then in step 4, evaluations are made based on the determined structure of the criteria. If the selected criterion has an objective structure, then crisp values are used, and the traditional TOPSIS model is applied. However, if the selected criterion has a subjective structure, then an extended TOPSIS model is applied in which probabilistic linguistic terms are used for evaluation. In this study, five main criteria were selected based on the literature review, and two of them are objective, whereas the rest are subjective. For that reason, for the determined two criteria, traditional TOPSIS steps are applied, and for the rest three criteria, an extended TOPSIS model is performed. Then, results are aggregated via considering the weights to obtain final CI values. Finally, all alternatives are ranked in descending order of CI values, and the best alternative is selected.

The location selection problem for plug-in-electric vehicles is very important, especially for crowded cities. This paper aims to evaluate the locations of possible charging stations in Istanbul, Turkey. The alternatives are compared by eight DMs based on their experience and beliefs via probabilistic linguistic terms set S, which is {S₀ = None, S₁ = Very Low, S₂ = Low, S₃ = Medium, S₄ = High, S₅ = Very High, S₆ = Perfect}.

Step 1. Firstly, alternatives are determined. Afterward, all of the districts in Istanbul are examined, and eight regions are chosen considering their geographical locations. Finally, as indicated in Fig. 3 and listed in Table 1, 39 alternative locations among the most preferred shopping malls are determined as the possible charging stations.

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Fig. 3

Alternative electric charging station locations in Istanbul.

Step 2. Five criteria are chosen by reviewing the literature. Two of them (capacity and flow density) are objective, whereas the rest (Accessibility, Closeness, and Attractiveness) are subjective. These selected criteria are:

Accessibility (a₁): Easiness of accessibility to the charging station

Capacity (a₂): Station capacity, which affects the waiting times of the vehicles that come to the station

Flow Density(a₃): Traffic flow density for serving more customers and providing a high utilization rate

Closeness (a₄): Closeness to residential areas

Attractiveness (a₅): Shopping centers’ favorability by customers

Step 3. Eight DMs evaluate the selected criteria to find their weights. Then, the decision matrix for groups is created and normalized (presented in the appendix Table A1). Therefore, final weights for all criteria are found as w₁ = 0.163; w₂ = 0.256; w₃ = 0.171; w₄ = 0.202; w₅ = 0.208, respectively. A sample calculation is given for the weight of accessibility (w₁ = 0.163) w 1 = ∑ i = 1 8 ∑ q ≠ i 1 6 ∑ k = 1 6 ( p i 1 ( k ) r i 1 ( k ) - p q 1 ( k ) r q 1 ( k ) ) 2 ∑ j = 1 5 ∑ i = 1 8 ∑ q ≠ i 1 6 ∑ k = 1 6 ( p ij ( k ) r ij ( k ) - p qj ( k ) r qj ( k ) ) 2 = 36.485 223.920 = 0.163

Step 4. Evaluation of the alternatives is examined separately according to different criteria types. For the determined two objective criteria (Capacity and Flow Density), traditional TOPSIS steps are applied, and for the rest three criteria (Accessibility, Closeness, and Attractiveness), extended TOPSIS model is applied since they are subjective. For this reason, step 4 is examined into two sub-parts.

Step 4.1. Initially, alternatives are examined according to capacity and flow density criteria, which are objective. The capacity of each shopping mall is listed. The flow density of the roads is analyzed using Traffic Flow values of the Istanbul Metropolitan Municipality. For the flow, density 1 and 5 represent the lowest and highest value, respectively. In the analyses, high density is considered as a benefit criterion since more customers can be served by the related location. Evaluations for both criteria are presented in Table 2.

After values are collected, traditional TOPSIS steps are applied. Firstly, all values are normalized and weighted. Weighted normalized matrix (presented in the appendix Table A2) is used to determine PIS and NIS values. For capacity, PIS = 0.232 and NIS = 0.012 . For flow density, PIS = 0.127 and NIS = 0.025.

According to the results obtained, the separation values of each alternative are calculated. Afterward, relative closeness values are achieved and presented in Table 3. A sample calculation for the first alternative is presented as follows. S * = ( 0.078 - 0.232 ) 2 + ( 0.051 - 0.127 ) 2 ) = 0.172 S - = ( 0.078 - 0.012 ) 2 + ( 0.051 - 0.025 ) 2 ) = 0.070 CI ( x 1 ) = 0.070 ( 0.172 + 0.070 ) = 0.290

Step 4.2. In the second sub-part, alternatives are examined according to accessibility, closeness, and attractiveness criteria, which are subjective. In the analysis, eight DMs provided the evaluations of the alternatives based on their experiences and beliefs via probabilistic linguistic terms set S, which is {S₀ = None, S₁ = Very Low, S₂ = Low, S₃ = Medium, S₄ = High, S₅ = Very High, S₆ = Perfect}. After evaluations are normalized, an ordered PLTS is achieved via arranging r^(k)p^(k) values in the descending order. A sample calculation for the first alternative is presented in Table 4. After all r^(k) and p^(k) values are calculated for each alternative, PIS and NIS for each attribute are obtained and provided as in Equations 6–7. L ( p ) + = ( { s 3.75 ; s 2.25 ; s 1.67 ; s 1.5 ; s 1 } , { s 3.75 ; s 2.25 ; s 2 ; s 1 ; s 1.2 } , { s 5.25 ; s 2.25 ; s 1.5 ; s 1 ; s 1 } )(6) L ( p ) - = ( { s 0.25 ; s 0 ; s 0 ; s 0 ; s 0 } , { s 0 ; s 0.17 ; s 0 ; s 0 ; s 0 } , { s 0 ; s 0 ; s 0 ; s 0 ; s 0 } )(7)

According to the obtained results in Step 3, each alternative’s deviation degree is computed and presented in Table 5. A sample calculation for the first alternative is presented in Table 4. For the first alternative d (x _i , L (p) ⁺) =0.167 + 0.197 + 0.326 = 0.690 and d (x _i , L (p) ^-) =0.151 + 0.251 + 0.169 = 0.571. All the other values are calculated with the same logic, and therefore, d _min  (x _i , L (p) ⁺) =0.528 and d _max  (x _i , L (p) ^-) =0.926 are determined. For each alternative, CI value is computed, and results are indicated in Table 5. A sample calculation is presented as follows. CI ( x 1 ) = 0.571 0.926 - 0.690 0.528 = - 0.690

Step 5. Since Conformity Index (CI) scores have different ranges for Classical TOPSIS and Probabilistic Linguistic TOPSIS, they are normalized before the aggregation. Although all the CI scores obtained from Classical TOPSIS are positive, negative CI scores are obtained as the result of Probabilistic Linguistic TOPSIS. Hence, proportion-based normalization is considered to be proper and applied as in Equation 8. NC i = ( C i - C i - ) / ( C j * - C j - )(8)

Where C i - is the smallest of the CI values, C j * is the biggest of the CI values.

Hence, the normalized CI values for crisp and fuzzy data are provided as in Table 6.

Step 6. Let NCI₁ and NCI₂ represent Normalized Conformity Indexes (NCI) of Classical TOPSIS and Probabilistic Linguistic TOPSIS, respectively, and w₁ and w₂ represent the total importance weights of the criteria analyzed by Classical TOPSIS and Probabilistic Linguistic TOPSIS, respectively. Then, Aggregated Normalized Conformity Index (ANCI) values are obtained via Equation 9 and shown in Table 7. ANCI = ( w 1 * NCI 1 + w 2 * NCI 2 ) / ( w 1 + w 2 )(9)

Steps 7-8. After the application of the methodology, the final ranking is obtained, and the best alternative is found as Meydan-BuYaka (x₁₅), as can be seen in Table 8.

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Table 8

Final ranks of the alternatives

/table>

However, region-based rankings can also be performed. For instance, the rankings for region 1 are given in Table 9. As can be seen in the results, Emaar (x₅) is the best, and Optimum (x₂) is the worst alternative in that region.

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Table 9

Ranks of the alternatives with respect to regions

#	Alternative	Rank	#	Alternative	Rank
X15	Meydan-Buyaka	1	X30	Marmara Park	21
X5	Emaar	2	X3	Palladium	22
X22	İstinyePark	3	X13	Maltepe Park	23
X14	Capitol	4	X32	Mall of İstanbul	24
X21	Kanyon	5	X24	Galleria	25
X4	Akasya	6	X20	Özdilekpark	26
X33	Forum İstanbul	7	X17	Kardiyum	27
X25	MarmaraForum	8	X31	Akbatı	28
X7	Watergarden	9	X2	Optimum	29
X35	Isfanbul	10	X29	Torium	30
X16	Metrogarden	11	X36	Akvaryum	31
X6	Hilltown	12	X28	Olivium	32
X19	Cevahir	13	X12	Marina	33
X8	Carrefour	14	X27	Historia	34
X26	Capacity	15	X10	Neomarin	35
X18	Akmerkez	16	X37	Atirus	36
X1	Tepe Natülüs	17	X11	Pendorya	37
X9	Viaport	18	X39	Maximall	38
X34	Venezia Mega	19	X38	Avlu34	39
X23	Metrocity	20

/table>

Currently, there are 26 electric charging stations in Istanbul based on the data of the Transport Management Center of Istanbul Metropolitan Municipality. Eight of these are located in shopping malls, and the rest are located in hotels, universities, parking centers, etc. Among mentioned 8 shopping malls, in Optimum (x₂), Palladium (x₃), Akasya (x₄), Pendorya (x₁₁), MaltepePark (x₁₃), Capitol (x₁₄), Meydan-Buyaka (x₁₅), Akbatı (x₃₁) there are already established charging stations. According to the proposed methodology, Meydan-Buyaka (x₁₅), Capitol (x₁₄), Akasya (x₄), Palladium (x₃), MaltepePark (x₁₃), Akbatı (x₃₁), Optimum (x₂), and Pendorya (x₁₁) are ranked as 1st, 4th, 6th, 22th, 23th, 28th, 29th, 37th, respectively in general ranking. In addition to the general ranking of the alternatives, region-based rankings are also obtained, as can be seen in Table 9. When the existing electric charging stations’ ranks are analyzed with respect to the regions, it is observed that three of the existing stations are from the first region, and their ranks in the region are 2nd, 7th and 8th. For the second region, the existing stations are ranked as 2nd and 5th. For the third region, the existing two stations are the 1st and 2nd. For the fourth and fifth regions, there is no existing station. For the sixth region, there is one existing station, and it is ranked as third. Finally, there is no existing station for the seventh and eighth regions.

Additionally, the results are analyzed considering the criteria weights. In this regard, attributes are selected one by one, and the weight of each selected attribute is changed while the rest maintained stable. In the analyses, three scenarios are generated for selected criterion’s different weights (0.1, 0.3, and 0.5, respectively) and the changes in the final order are observed. Therefore, 15 different scenarios are tested. The results of the first scenario considering the first three alternatives, are depicted in Fig. 4. It is obtained that the rankings do not change when the importance weights of the first criterion are 0.3 and 0.5. However, the first and second alternatives’ order replaces when the criterion importance weight is 0.1. Detailed results of all scenarios are given in Table 10.

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Fig. 4

The first three alternatives in scenario 1.

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Table 10

Results of the sensitivity analysis

Region #		Alternative	Final rank	Regional rank	Region	Alternative	Final rank	Regional rank
1	X5	Emaar	2	1	5	X25	Marmara Forum	8	1
	X 4	Akasya (*)	6	2		X26	Capacity	15	2
	X7	Watergarden	9	3		X24	Galleria	25	3
	X6	Hilltown	12	4		X28	Olivium	32	4
	X8	Carrefour	14	5		X27	Historia	34	5
	X1	Tepe Natülüs	17	6	6	X30	Marmara Park	21	1
	X 3	Palladium (*)	22	7		X32	Mall of İstanbul	24	2
	X 2	Optimum (*)	29	8		X 31	Akbatı (*)	28	3
2	X9	Viaport	18	1		X29	Torium	30	4
	X 13	Maltepe Park (*)	23	2	7	X33	Forum İstanbul	7	1
	X12	Marina	33	3		X35	Isfanbul	10	2
	X10	Neomarin	35	4		X34	Venezia Mega	19	3
	X 11	Pendorya (*)	37	5		X36	Akvaryum	31	4
3	X 15	Meydan-Buyaka (*)	1	1	8	X37	Atirus	36	1
	X 14	Capitol (*)	4	2		X39	Maximall	38	2
	X16	Metrogarden	11	3		X38	Avlu34	39	3
	X17	Kardiyum	27	4
4	X22	İstinyePark	3	1
	X21	Kanyon	5	2
	X19	Cevahir	13	3
	X18	Akmerkez	16	4
	X23	Metrocity	20	5
	X20	Özdilekpark	26	6	(*) indicates the existing electric charging stations

Rank	Case w1			Case w2			Case w3			Case w4			Case w5
	0.1	0.3	0.5	0.1	0.3	0.5	0.1	0.3	0.5	0.1	0.3	0.5	0.1	0.3	0.5
1	X15	X5	X5	X5	X15	X15	X15	X15	X15	X15	X15	X5	X15	X15	X5
2	X5	X15	X15	X15	X5	X35	X5	X5	X35	X5	X5	X15	X5	X5	X15
3	X22	X22	X22	X22	X22	X33	X22	X22	X33	X22	X22	X22	X22	X22	X22
4	X14	X14	X21	X14	X14	X5	X14	X33	X22	X33	X14	X21	X33	X14	X21
5	X33	X21	X14	X21	X33	X22	X21	X35	X5	X14	X21	X14	X14	X21	X14
6	X21	X4	X4	X4	X21	X25	X4	X14	X25	X4	X4	X4	X4	X4	X4
7	X4	X7	X7	X7	X4	X4	X33	X4	X34	X21	X33	X7	X21	X33	X7
8	X25	X25	X6	X25	X25	X34	X25	X25	X4	X25	X7	X25	X25	X25	X25
9	X35	X33	X25	X33	X35	X14	X7	X21	X14	X35	X25	X6	X35	X7	X6
10	X7	X6	X18	X6	X7	X21	X6	X7	X21	X7	X6	X18	X7	X6	X18
11	X16	X16	X19	X19	X16	X9	X16	X34	X9	X16	X16	X19	X16	X16	X33
12	X6	X19	X26	X18	X6	X7	X19	X16	X30	X34	X19	X33	X34	X19	X19
13	X19	X26	X16	X16	X19	X30	X26	X9	X32	X8	X26	X16	X8	X26	X16
14	X8	X18	X33	X26	X8	X32	X8	X8	X7	X6	X8	X26	X6	X8	X26
15	X26	X8	X8	X8	X26	X16	X18	X19	X16	X19	X18	X8	X19	X18	X8
16	X34	X1	X23	X1	X34	X8	X35	X6	X8	X9	X35	X23	X9	X35	X23
17	X9	X35	X1	X23	X9	X19	X1	X26	X31	X26	X1	X1	X26	X1	X1
18	X1	X23	X3	X3	X1	X26	X23	X30	X19	X1	X23	X3	X1	X23	X3
19	X18	X9	X20	X9	X18	X1	X9	X1	X26	X30	X9	X20	X30	X9	X20
20	X30	X3	X24	X35	X30	X6	X3	X32	X1	X18	X3	X24	X18	X3	X9
21	X23	X13	X9	X20	X23	X31	X34	X18	X6	X32	X34	X9	X32	X34	X24
22	X32	X20	X13	X24	X32	X13	X13	X13	X13	X3	X13	X13	X3	X13	X13
23	X3	X24	X17	X13	X3	X18	X30	X3	X3	X23	X20	X17	X23	X30	X17
24	X13	X34	X2	X17	X13	X3	X20	X23	X18	X13	X30	X35	X13	X20	X35
25	X24	X30	X35	X2	X24	X17	X24	X31	X17	X24	X24	X2	X24	X24	X2
26	X20	X17	X28	X30	X20	X24	X17	X24	X29	X17	X17	X28	X31	X17	X28
27	X17	X32	X30	X34	X17	X23	X32	X17	X24	X31	X32	X30	X17	X32	X30
28	X31	X2	X36	X28	X31	X29	X2	X20	X23	X20	X2	X36	X20	X2	X36
29	X2	X28	X34	X32	X2	X20	X28	X29	X20	X29	X28	X34	X29	X28	X34
30	X29	X36	X32	X36	X29	X2	X31	X2	X2	X2	X36	X32	X2	X31	X32
31	X36	X29	X29	X29	X36	X36	X36	X36	X36	X36	X31	X29	X36	X36	X29
32	X28	X31	X31	X31	X28	X28	X29	X28	X28	X28	X29	X31	X28	X29	X31
33	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12	X12
34	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27	X27
35	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10	X10
36	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37	X37
37	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11	X11
38	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39	X39
39	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38	X38