Electric Vehicle Solar Charging Station Siting Study Based on GIS and Multi-Criteria Decision-Making: A Case Study of China

Abstract

Electric vehicles (EVs) are one of the most practical solutions to the energy issue and environmental pollution. In recent years, EVs have developed rapidly, but are still limited by charging problems. The emergence of photovoltaic charging stations can solve the environmental pollution and charging problems. The location of charging stations is critical in the life cycle of electric vehicles. In this paper, a multiple-criteria decision-making (MCDM) method based on Geographic Information Technology (GIS) for optimal site selection is proposed. First, based on literature reading and expert interviews, a site selection index system was identified, including four aspects with a total of ten sub-criteria. Secondly, a spatial database of relevant evaluation criteria was established using GIS, and preliminary analysis was conducted. Then, the fuzzy DEMATEL (Decision-Making Trial and Evaluation Laboratory method) is applied for assigning the criteria weights. Then, potential sites are ranked using the fuzzy MULTIMOORA (Multi-Objective Optimization on the basis of Ratio Analysis) method. Then, the model was validated by siting the electric vehicle PV charging stations in Qingdao, and eight stations were identified in the preliminary selection stage, and the most suitable locations were finally selected through the MCDM stage. Finally, the reliability and validity of the model were further verified by comparative analysis and dual sensitivity analysis.

1. Introduction

With the global economy’s rapid growth and the shortage of natural resources, the energy crisis and environmental degradation have caused sustainable development problems in various countries [1,2]. IThe robustness of the transportation sector is one of the key reasons for the high energy consumption and carbon emissions [3], as shown in Figure 1 (data source: https://www.carbonmonitor.org.cn, accessed on 6 July 2022). As a result, countries have adopted different strategies to solve the energy crisis and pollution problems. In transportation, EVs are strongly supported because of the advantages of energy saving, emission reduction, and pollution reduction [4,5,6]. EVs instead of conventional fuel vehicles can significantly reduce carbon emissions [7] and promote sustainable development in the world.

EVs are developing at a rapid rate, but there are still some problems with their battery life and charging [8]. Electric vehicle charging stations (EVCS), as the energy suppliers for EVs, are the basis for the transition of the transport sector in a sustainable direction. Even with a very high market penetration of EVs, the overall impact on annual energy consumption is anticipated to be minimal given that coal is still the main energy source used in the power generation sector of the Chinese power system [9]. The aforementioned issues have facilitated the formation of photovoltaic (PV) charging stations (PVCS), that is, the effective combination of PV power generation with charging stations for electric vehicles [10]. PV charging stations can truly achieve zero emissions and pollution, and eliminate the dependence of ordinary electric vehicles on fossil fuels.

The construction of urban energy supply facilities directly reflects the degree of sustainable development of urban transportation. In addition, convenient and efficient energy supply methods can promote people’s desire to purchase electric vehicles [11]. Therefore, in the face of the increasing abundance of EVs, the layout of PVCS in urban areas is crucial to the development of EVs, and investigation into the location of PVCS is required. In addition, it is found through the literature studies that most of the PVCS sites are for traditional electric vehicle power stations and lack completeness at the initial selection stage.

Based on the above motivations, this study developed a GIS-based MCDM method to determine the optimal placement for PVCS. First, upon the geographic information data (land type, distribution of roads, point of interest (POI) distribution, etc.,) of the study area, a visual suitability analysis map is generated using GIS, from which an area with higher suitability is selected. Secondly, the evaluation criteria system of the MCDM part was established through relevant literature and survey reports. The criteria system includes four criteria and 10 sub-criteria, covering four aspects of economy, society, technology, and nature. The index weights are then determined by combining the triangular fuzzy number with the DEMATEL. The introduction of triangular fuzzy numbers can convert uncertain language into quantitative information, which can effectively deal with the fuzziness and uncertainty of evaluation scoring caused by subjective judgment of experts. The DEMATEL model can not only show the overall influence degree of each factor better, but also visualize the causal relationship between factors in the system in the form of relationship diagram [12]. The schemes are ranked using the MULTIMOORA method, which is based on triangular fuzzy numbers and consists of three sub-methods: the ratio system method, the reference point method, and the complete phase multiplication method. Finally, the three results are combined using the ordinal dominance theory. The fuzzy MULTIMOORA method is highly stable, comprehensive, understandable, and able to fully take into account the ambiguity of the data, integrating the three sub-methods, avoiding the one-sidedness of the single decision method in the traditional MCDM method, and providing correct and reliable results [13]. Figure 2 depicts the framework for this paper’s research. Its innovation points are summarized as follows:

(1) The evaluation index system of two stages of EV PV charging station siting is established, which fully considers both sustainable development perspective and basic conditions, and improves the integrity of the primary selection stage of charging station siting research.

(2) For the first time, GIS is combined with the fuzzy DEMATEL-MULTIMOORA method to fully consider both qualitative and quantitative factors, which improves the visualization of the siting problem and enriches the research ideas in this field.

(3) Comparative analysis and dual sensitivity analysis were carried out to further determine the stability and validity of the research model. The fluctuation of index weights and the number of experts set in the sensitivity analysis stage make up for the shortage of initial information that changes with relevant literature or experts.

The rest of this paper is organized as follows. Section 2 reviews the characteristics and shortcomings of charging station siting studies and the literature related to the main applications of MCDM methods combined with GIS. Section 3 describes the methodology used in this study and identifies the site selection evaluation index system. Section 4 validates the model with an example of EV PVCS siting in Qingdao. Section 5 is a further validation of the proposed methodology of this study through comparative analysis and dual sensitivity analysis. Section 6 concludes the study and indicates the direction for future research.

2. Literature Review

2.1. Study on Site Selection of Charging Stations

Many studies in the early stages of EV development were mostly on technology [14,15] and economy [16,17,18]. With the development of EVs, experts realize that cruising range is a key issue, so it is necessary to study more suitable energy replenishment methods. Most of this is the study of the location of charging stations, and the other part is the study of charging methods [19,20].

Most of the research on charging station siting adopts a MCDM approach. Guo et al. (2015) proposed the fuzzy TOPSIS approach to choose the best EVCS site and for the first time from the standpoint of sustainable development established the sustainability rating index of EVCS site selection problem [21]. Wu et al. (2017) introduced the target community situation when establishing the evaluation index system, adopted a comprehensive method to find out the subjective and objective weights, and used the TOPSIS to rank the scheme [22]. Liu et al. (2019) handled the issue of charging station site selection by integrating the MCDM method of UL-MULTIMOORA with DEMATEL and verified its effectiveness with a case [23]. Wang et al. (2023) introduced heterogeneous information and multi-granularity language terminology for sustainable charging station site selection when collecting qualitative data [24].

In addition, there are studies that employ optimization models to tackle the problem of charging station site selection. Sadeghi et al. (2014) proposed a mixed integer nonlinear (MINLP) optimization method to achieve optimal sites and sizes for EV fast charging stations [25]. Tu et al. (2016) proposed a spatio-temporal demand coverage method to optimize the placement of electric rental car charging stations in a spatio-temporal environment [26]. Hosseini (2019) et al. used Bayesian network models to study the location of charging stations, and emphasized that charging stations are fast charging stations [1]. Zhang et al. (2022) combined GIS and Bayesian networks (BN) to deal with the electric vehicle location selection problem [27]. Using MATLAB and YALMIP language editors, Zu et al. (2022) solved the problem of charge station site selection by developing a multi-objective location optimization model with the objectives of minimizing the total construction cost and maximizing user satisfaction [28]. Zhou et al. (2022) developed a genetic algorithm-based charge station location optimization model based on total social cost [29].

Considering the sustainability of photovoltaic power generation, there have been many studies in recent years to combine photovoltaic power generation with charging stations. Tulpule et al. (2013) demonstrated the feasibility of a PV-based charging station with an economic analysis and carbon emission analysis [30]. Shepero et al. (2018) performed spatio-temporal modeling of photovoltaic power generation and electric vehicle charging, identifying research gaps for further exploration [31]. Zhou et al. (2020) integrated GIS and MCDM to establish a site selection system for PVCS [32]. Dang et al. (2021) investigated the site selection of PVCS for island ships using the hybrid fuzzy VIKOR method [33]. To determine the service radius, ideal location, and scale of fast-charging stations, solar plants, and battery energy storage systems, Kumar et al. (2022) suggested a two-phase multi-objective planning framework [34].

In summary, we can conclude that most of the research on charging station site selection is based on traditional EVCS, and these studies provide a rich theoretical model for this paper. There are currently few studies on the location of PVCS, and most of the alternative sites are fictitious, so the research lacks a certain completeness. Consequently, this paper will employ GIS to examine the location determination of urban PVCS.

2.2. GIS Is Combined with MCDM

Environmental factors, economic factors, social factors, and technical factors, among others, will influence the location decision of charging stations, making the location problem of EVCS a multi-attribute decision-making problem. As a mature location analysis technology, GIS has been extensively utilized in numerous disciplines. As a result, the integration of GIS and MCDM will be covered in this paper. As a powerful geographic information processing system, GIS is often used in the preliminary selection stage of site selection problems. The powerful geographic analysis capabilities of GIS can help scholars narrow down the scope of research and reduce site selection costs. The MCDM method is used for further selection, and the optimal site selection results are obtained by weighting the evaluation criteria and ranking the schemes.

In site selection decision analysis, the combination of GIS and MCDM has been widely used. Zhang et al. combined GIS with MCDM for landfill site selection, and used the Harlingen landfill in South Texas as a case study for verification [35]. Sanchez et al. (2013) [36] and Al Garni et al. [37] (2017) selected solar power plant locations using GIS-AHP methods. Villacreses et al. (2015) utilized the GIS-AHP-TOPSIS method to determine wind farm site suitability [38]. Kabak et al. (2018) investigated bike-sharing locations utilizing a combination of GIS, AHP, and MOORA techniques [39]. Based on the above research, it can be seen that the combination of these two methods has been very mature and effective in all aspects.

In order to make the location decision findings more rigorous and serve as a guide for the location selection of PVCS, this study fully utilizes the benefits of GIS and combines them with the fuzzy DEMATEL-MOLTIMOORA approach.

3. Research Model

3.1. Site Selection Evaluation Index System

Evaluation criteria play a crucial role in the selection of EVCS sites. In order to make the study more comprehensive, qualitative and quantitative factors should be considered together. Many academics have researched the elements of EVCS siting in order to develop a reasonable assessment criteria system.

Table 1. Evaluation indicators for siting charging stations and PVCS.

Literature	Year	Research Topics	Factors
[21]	2015	Site selection for EV charging stations	Environmental criteria: extent of vegetation and water damage, waste emissions, reduction of greenhouse gas emissions, reduction of fine particulate matter Economic criteria: cost of construction, annual operating and maintenance costs, payback period Social criteria: coordination, accessibility, service capacity, impact on people’s lives
[23]	2018	Site selection for EV charging stations	Environmental criteria: extent of vegetation and water damage, waste emissions, reduction of air pollutants Economic criteria: project cost, annual costs for operation and maintenance Social criteria: coordination, accessibility, service capacity, impact on people’s life
[40]	2018	Site selection for EV charging stations	Environmental criteria: degree of damage to vegetation and water bodies, electromagnetic interference, ecological impact Economic criteria: overall construction costs, annual costs for operation and maintenance, renewal and demolition costs, projected annual economic benefits Social criteria: coordination with urban development plans, accessibility, electric vehicle ownership in the target area Technical criteria: impact on grid safety, substation capacity permit, voltage stability
[1]	2019	Site selection for EV charging stations	Environmental criteria: air quality, waste emissions, damage to water resources Economic criteria: land cost, construction cost, maintenance cost Social criteria: accessibility, service level, population density, location safety and security Technical criteria: power outage (downtime)
[32]	2020	EV PVCS site selection	Natural criteria: direct normal exposure, average annual temperature Economic criteria: payback period for construction costs Technical criteria: impact on the grid, possibility of future capacity expansion Social criteria: government support, public acceptance
[41]	2022	EV PVCS site selection	Accessibility criteria: major roads, major squares, major intersections, major junctions Proximity criteria: residential areas, public buildings, gas stations, public parking lots, airports and seaports Technical criteria: global horizontal irradiance

provides a summary of the evaluation indices for the placement of charging stations and PV charging stations. In addition, the evaluation criteria were determined by collecting experts’ opinions (experts from ecological and environmental departments, transportation departments, natural resources departments, PV power plant companies, charging station companies, and related field studies). Based on the relevant literature and expert interviews and combined with the Chinese national conditions, the evaluation index system was divided into four aspects, including economic index B1, social index B2, technical index B3, and natural index B4, as shown in Figure 3.

3.2. Research Method

3.2.1. Geographic Information System (GIS)

GIS is a computer technology system based on geospatial databases. GIS has five functions: data collection and analysis, data storage and management, data conversion and processing, spatial query and analysis, and visual expression and output [42]. Due to its advantages in spatial information management and analysis, GIS is utilized extensively in many disciplines, including military management, energy site selection, land management, traffic management, environmental monitoring, government work, etc. [43,44,45,46,47].

GIS can manage and analyze data, visually express them, and provide decision-making support for decision makers. Therefore, ArcGIS10.7 software was used for the preliminary analysis of site selection. The main steps are as follows.

First, establish the criteria for the GIS analysis stage and collect data; the standards are shown in

Table 2. Criteria for the GIS analysis stage.

Factors	Interpretation
Type of land	There are forests, shrubs, man-made land, meadows, farmland, and other types. Different types of land are suitable for building PVCS. The study set ten scoring levels, with higher suitability land types with higher score [48]
Road distribution	For transportation reasons, the area closer to the main road is more suitable.
Waterway distribution	For safety reasons, the construction of PVCS should be kept away from water sources. Therefore, areas farther away from water sources score higher.
Distribution of gas stations	For safety and road traffic reasons, PVCS should be separated from gas stations, so the area farther away from gas stations in the analysis scored higher.
Points of interest (POI)	POI generally signifies the point data in the Internet electronic map, which means tourist attractions, commercial points, companies, transportation facilities, and other places, such as schools, hotels, parks, etc. The more points of interest, the greater the traffic flow [49]. Therefore, the more points of interest, the higher the zone suitability score.
Distribution of existing charging stations	Due to the convenience of construction, the closer the area to the existing ordinary charging station, the higher the suitability score, since PVCS can be retrofitted and expanded on the basis of existing charging stations.

. The distance of road distribution, waterway distribution, petrol station distribution, POI distribution, and existing charging stations is analyzed in the second phase. The distance analysis method used in this study is Euclidean distance analysis, which expresses the straight-line distance between two cells. The third step is to use a 10-point scale to reclassify land types, road distribution, gas station distribution, and POI distribution. At this stage, a ten-point scoring system is utilized, with the score increasing as suitability increases. The fourth step is overlay analysis. In this study, we used raster data overlay during the data overlay analysis phase. A raster data structure is a commonly used geospatial data structure. Raster cells are the basis for describing information in raster data, and individual cells express point elements, points form lines, and lines form polygons. The overlay of raster data is to copy the location and attributes of the cells of each data layer, and the overwritten attribute values are obtained by the collection operation of the overlay operator, resulting in a new layer. The six factors in the overlay analysis are given different weights, and the weighting formula is as follows to form an intuitive map. Finally, the area with a high comprehensive score is selected as an alternative site for the construction of PVCS for electric vehicles.

$$\mathrm{Suitability}={\alpha }_1\mathrm{Reclassland}+{\alpha }_2\mathrm{Reclassroad}+{\alpha }_3\mathrm{Reclasswater}+{\alpha }_4\mathrm{Reclassgas}+{\alpha }_5\mathrm{ReclassPOI}+{\alpha }_6\mathrm{Reclassstation}$$

(1)

where ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, ${\alpha }_4$, ${\alpha }_5$ and ${\alpha }_6$ represent the weight of these six factors and ${\alpha }_1+{\alpha }_2+{\alpha }_3+{\alpha }_4+{\alpha }_5+{\alpha }_6=1$.

3.2.2. Fuzzy DEMATEL

DEMATEL is a method for analyzing factors in complex systems proposed by professors Gabus and Fontela [50] at the GeEVa Research Center. Based on graph theory, this method builds a structural analytical model to recognize the causal relationship between complex factors and identify key elements [51], and has been applied to many fields [52,53]. In this paper, the triangular fuzzy number (TFN) is introduced on the basis of the DEMATEL method to quantify the qualitative evaluation of the influence of various factors in the location of PVCS, and the fuzzy number is converted into a clear value by deblurring. In order to better illustrate the steps, two definitions are clarified.

Definition 1. 

A fuzzy number $M=\left(l,m,u\right)$ is considered a TFN if its membership function satisfies ${\mu }_M\left(x\right)$.

$${\mu }_M(x)=\left\{\begin{array}{cc}0& x<l,x>u\\ \frac{x-l}{m-l}& l\le x\le m\\ \frac{u-x}{u-m}& m\le x\le u\end{array}\right.$$

(2)

where $x\in R$, $l,m,u$ are real numbers and $l\le m\le u$, $l,u$ are the minimum and maximum values for $M$. Figure 4 can explain the geometric relationship of the triangular fuzzy numbers.

Definition 2. 

The finite set of ordered language items with inhomogeneous elements is $S=\left(s_0,s_1,\dots s_{(n/2)-1},s_{n/2},s_{(n/2)+1},\dots ,s_n\right)$, where n is an even number and $S_i$ is the $\left(i+1\right)$th linguistic term. Then for a given language term $S$, you can use Formula (3) to convert the language term $S_i$ to the corresponding TFN:

$$M_{S_i}=\left(l,m,u\right)=\left(\max \left\{\frac{i-1}{n},0\right\},\frac{i}{n},\min \left\{\frac{i+1}{n},1\right\}\right),fori=(0,1,\cdots ,n)$$

(3)

The steps are as follows:

Step 1: Experts are invited to rate the degree of mutual influence between the criteria, $c_{ij}$ indicates the degree of direct influence of indicator $c_i$ on indicator $c_j$, and the elements on the main diagonal are specified to be zero to obtain the initial evaluation matrix of the indicators ${\left[C_{ij}\right]}_{n\times n}$.

There are five levels of impact: no effect (N), very low impact (VL), low impact (L), high impact (H), and very high impact (VH).

Step 2: Calculate the direct relationship matrix based on the TFN.

In accordance with Formula (3), the TFN corresponding to the expert semantic variable is determined, as can be seen in

Table 3. Semantic variables and corresponding TFN.

Linguistic Terms	N	VL	L	H	VH
TFN	[0, 0, 0.25]	[0, 0.25, 0.5]	[0.25, 0.5, 0.75]	[0.5, 0.75, 1]	[0.75, 1, 1]

. Using the method of averaging, the mutual influence relationship of the indicators provided by the expert is aggregated, and the overall triangular fuzzy direct relationship matrix ${\otimes G}_k={\left[{\otimes g}_{ij}^k\right]}_{nxn}$ is generated.

Step 3: Obtain the complete direct-relation matrix.

The complete direct correlation matrix is de-blurred and transformed into a clear direct correlation matrix $G_k={\left[g_{ij}^k\right]}_{nxn}$ by Formula (4).

$$S({\rm M})=\frac{l+2m+u}{4}$$

(4)

Step 4: Normalize the matrix G. If the direct impact matrix after normalization is P, its equation is:

$$P=G/\underset{1<i<n}{\max }\sum {\mathrm{g}}_{ij}$$

(5)

Step 5: Construct the combined impact matrix T. The specific formula is:

$$T={(t_{ij})}_{(n\times n)}=\underset{h\to \infty }{\lim }(P+P^1+P^2+\cdots +P^r)=P{(E-P)}^{-1}$$

(6)

where E is a unity matrix, and when $r\to \infty$, $P^r=0$ is satisfied.

Step 6: Solve the centrality and causality of each indicator.

$$e_i={\displaystyle \sum _{i=1}^n{t}_{ij}},f_j={\displaystyle \sum _{j=1}^n{t}_{ij}}$$

(7)

where $i=j$, the centrality of the index C_i is $f_{\dot{l}}+e_i$ (the relative significance of the indicator C_i to the system as a whole), and the causal degree is $f_i-e_i$ (the causal logical relationship between the indicator C_i and other indicators).

Step 7: Calculate the weight of each indicator:

$${\omega }_i=\frac{\sqrt{{(f_i+e_i)}^2+{(f_i-e_i)}^2}}{{\displaystyle \sum _{i=1}^n\sqrt{{(f_i+e_i)}^2+{(f_i-e_i)}^2)}}}$$

(8)

3.2.3. Fuzzy MULTIMOORA

The MULTIMOORA method is a multi-objective optimization model created by Brauers and Zavadskas in 2010 [54], including the ratio system method, the reference point method, and complete multiplication. This approach can rank schemes according to the results of three dependent methods. In this study, the MULTIPMOORA method based on TFN will be used to rank the alternatives. The procedure is as follows:

Step 1: Create the preliminary assessment matrix.

We determine the quantitative criterion’s baseline data through the relevant reports and obtain the initial information of the qualitative criteria through expert evaluation. Then we obtain the initial evaluation matrix $D_k={\left[d_{ij}^k\right]}_{n\times m}$. The information obtained has three forms: clear value, period value, and language term.

Step 2: Establish a triangular fuzzy evaluation matrix $P_k={\left[{\tilde{p}}_{ij}^k\right]}_{nxm}$.

This involves converting clear values, period values, and linguistic terms to TFN. The conversion method is as follows: The clear value can be converted to three equivalent values of TFN. The clear value 2.6, for instance, can be transformed to TFN (2.6, 2.6, 2.6). When the interval value is converted to TFN, the median value is determined by averaging the interval’s upper and lower boundaries [55]. For example, interval values (3, 7) can be converted to (3, 5, 7). Use Equation (3) to convert linguistic terms to TFN.

The appropriate semantic scale should be determined for the evaluation of expert language terms, as shown in

Table 4. Language evaluation values and corresponding TFN.

Influence	Abbreviation	TFN
Very Low	VL	(0, 0, 0.167)
Low	L	(0, 0.167, 0.333)
Moderately Low	ML	(0.167, 0.333, 0.5)
Medium	M	(0.333, 0.5, 0.667)
Moderately High	MH	(0.5, 0.667, 0.833)
High	H	(0.667, 0.833, 1)
Very High	VH	(0.833, 1, 1)

.

Step 3: Obtain a comprehensive TFN decision matrix.

Here, we employ the FOWA operator to combine the expert judgements because the evaluation values provided by various experts differ. First, calculate the vector $\overline{{\omega }_h}$ according to the Formulas (9) and (10). Then deblurring occurs according to Formula (4). Finally, according to Formula (11), the comprehensive TFNs decision matrix $P={\left[p_{ij}\right]}_{nxm}$ is obtained.

Let Q be a proportional language that does not decrease with the following calculation:

$$Q(z)=\left\{\begin{array}{cc}0& z<a\\ \frac{z-a}{b-a}& a\le z\le b\\ 1& z>b\end{array}\right.$$

(9)

where $a,b,z\in \left[0,1\right]$ and satisfy the ambiguous semantic quantization criterion: “most”, “at least half”, “as much as possible”, and $\left(a,b\right)$ are (0.3,0.8), (0,0.5), and (0.5,1) respectively. Then the aggregate weighted vector $\omega$ is equal to

$$w_j=Q\left(\frac{j}{n}\right)-Q\left(\frac{j-1}{n}\right),j=1,2,\dots ,n$$

(10)

If the following conditions are met by the function f, we describe it as an n-dimensional triangular fuzzy ordered weighted average (FOWA) operator:

$$f:R^n\to R,f\left(a_1,\dots ,a_n\right)={\displaystyle \sum _j{w}_j}{\tilde{b}}_i$$

(11)

where $w$ is the connected weighted vector to f and $w={\left(w_1,w_2,\cdots ,w_n\right)}^T$, $w_j\in \left[\mathrm{0,1}\right]$, ${\Sigma }_j{w}_j=1$, the i th biggest element in a triangular fuzzy set of $\widetilde{{\alpha }_i}\left(i=\mathrm{1,2},\cdots ,n\right)$ is $\widetilde{b_i}$.

Step 4: Standardize the exhaustive TFN decision matrix.

The greater the value of the benefit criterion, the higher the scheme’s suitability. The lower the value of the cost criterion, the higher the suitability of the scheme. Matrix normalization is required to eliminate the influence of different attributes of the indicators on the final evaluation value. Matrix normalization can eradicate the impact of varying measurement dimensions, and normalize the process through Equation (12) to obtain the normalized matrix $S={\left[s_{ij}\right]}_{n\times m}$.

$$\left(s_{ij}^l,s_{ij}^m,s_{ij}^u\right)=\left\{\begin{array}{l}\left(\frac{p_{ij}^l}{p_{{\max }^u}},\frac{p_{ij}^m}{p_{{\max }^u}},\frac{p_{ij}^u}{p_{{\max }^u}}\right)\mathrm{for}\mathrm{benefit}\mathrm{criteria}\hfill \\ \left(\frac{p_{\min j}^l}{p_{ij}^u},\frac{p_{\min j}^l}{p_{ij}^m},\frac{p_{\min j}^l}{p_{ij}^l}\right)\mathrm{for}\cos t\mathrm{criteria}\hfill \end{array}\right.$$

(12)

where $p_{\mathit{max} j}^u=\mathit{max}\left\{\left.p_{ij}^u\right|i=\mathrm{1,2},\cdots ,m\right\}$ and $p_{\mathit{min} j}^l=\mathit{min}\left\{\left.p_{ij}^l\right|i=\mathrm{1,2},\cdots ,m\right\}$.

Step 5: The weighted ratio system based on TFN.

In this approach, the greater the $v_i$ of the assessment, the better the corresponding alternative.

$$v_i={\displaystyle \sum _{j=1}^n{w}_j}{s}_{ij}$$

(13)

Step 6: TFN-based reference point methodology.

Initially, the elements in the matrix S are de-blurred according to Formula (4), and the TFN of each indicator is sorted on this basis, and the maximum value is chosen as the benchmark. Then calculate the distance $d_{ij}=d\left(s_{ij},s_j^{*}\right)$ between each assessment value and the reference point according to Formula (14).

$$d(a,b)=\sqrt{\frac{{\left(a^l-b^l\right)}^2+{\left(a^m-b^m\right)}^2+{\left(a^u-b^u\right)}^2}{3}}$$

(14)

where $a,b$ are TFN, $a=\left(a^l,a^m,a^u\right),b=\left(b^l,b^m,b^u\right)$.

The estimated value for each alternative under the method is then calculated.

$$d_i={\displaystyle \sum _{j=1}^n{w}_j{d}_{ij}}$$

(15)

Obviously, the smaller the estimate in the reference point method, the better the scheme’s suitability.

Step 7: Complete multiplication form based on TFN.

Using the procedure below, the predicted value for each alternative $u_i$ was determined.

$$u_i={\displaystyle \prod _{j=1}^n{\left(s_{ij}\right)}^{w_j}}$$

(16)

The value $u_i^{\prime }$ is obtained after deblurring with Formula (4).

Step 8: Obtain the final rankings for the available options. By combining the ranking outcomes of the alternatives under the three sub-methods using the ordinal dominance theory, the final scheme ranking can be derived.

The theory of ordinal number dominance includes three cases: absolute dominance, general dominance, and equalization. To illustrate, suppose there are four numerical rankings $x>y>z>k$. If the ranking of scheme A is $\left(x,x,x\right)$, then scheme A is absolutely superior; if the ranking of scheme A is $\left(x,x,k\right)$ and the ranking of scheme B is $\left(y,y,z\right)$, then scheme A is generally superior to B. Since the ordinal dominance theory has transferability, if the ranking of scheme A is superior to that of scheme B, the ranking of scheme B is superior to that of scheme C, and the ranking of scheme C is superior to that of scheme A, then the three schemes are judged to be equal.

4. Case Studies

4.1. Overview of the Study Area

Qingdao is a tourist city and has a rapid economic development, so the demand for transportation construction is high. Since China included new energy charging facilities in key areas, Qingdao has adhered to the work idea of adapting measures to local conditions, and has intelligently, efficiently, and vigorously promoted the construction of EV charging facilities, and continuously improved the market scale and service quality. A corporation intends to make investments in the building of an electric vehicle PVCS in Qingdao based on market demand and policy, and uses the site selection model established in this paper to select the site of PVCS. Figure 5 depicts the geographic location of Qingdao and its solar energy resources.

4.2. GIS Processing Stage

The initial data of the GIS processing stage were obtained from the Planning Cloud website, the OSM website, and the Resource Environment and Science Center, and then loaded into ArcGIS 10.7 program for visualization, and the processing results are shown in Figure 6. Then, the Euclidean distance analysis described in Section 3.2.1 and reclassification were applied to perform suitability analysis, and the analysis results are shown in Figure 7.

Then the superposition analysis was carried out, and the standard weights in Formula (1) are determined by expert scoring as follows: ${\alpha }_1$ = 0.3, ${\alpha }_2$ = 0.2, ${\alpha }_3$ = 0.1, ${\alpha }_4$ = 0.1, ${\alpha }_5$ = 0.1, ${\alpha }_6$ = 0.2. As depicted in Figure 8, eight areas with high suitability scores were selected as potential PVCS construction sites. A1 is close to Yantai Road, Laixi City; A2 is close to Longquan River Bridge, Jimo District; A3 is close to Zhengyang Road, Chengyang District; A4 is close to Chunyang Road, Chengyang District; A5 is close to Chongqing North Road, Chengyang District; A6 is close to Hongkong Middle Road, Shinan District; A7 is located near Jiangshan North Road, Huangdao District; and A8 is located near Lijiang East Road, Huangdao District.

4.3. Determine Index Weight

The site selection of Qingdao electric vehicle PVCS mainly includes four standards and 10 sub-standards. First, 27 experts in the fields of environment, economy, society, electricity, and transportation were invited to evaluate the impact relationship between different indicators, and an initial direct relationship matrix was obtained. Secondly, a single fuzzy direct relationship matrix can be obtained from Table 3, and then the complete triangular fuzzy direct relationship matrix can be obtained by the averaging method. In the third step, according to Formula (4), the overall brittle straight relationship matrix is obtained after deblurring. Then, according to Formulas (5)–(8), the normative direct impact matrix, the comprehensive impact matrix (

Table 5. Composite impact matrix.

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
C1	0.285	0.478	0.486	0.267	0.517	0.417	0.35	0.453	0.057	0.058
C2	0.36	0.332	0.475	0.279	0.511	0.454	0.371	0.42	0.056	0.058
C3	0.276	0.295	0.222	0.197	0.333	0.306	0.231	0.292	0.042	0.043
C4	0.411	0.434	0.4	0.232	0.52	0.497	0.282	0.41	0.056	0.057
C5	0.447	0.538	0.502	0.38	0.454	0.564	0.429	0.539	0.065	0.067
C6	0.316	0.371	0.359	0.336	0.447	0.316	0.285	0.419	0.051	0.053
C7	0.376	0.467	0.396	0.26	0.498	0.504	0.269	0.486	0.057	0.058
C8	0.246	0.272	0.298	0.208	0.342	0.319	0.255	0.233	0.042	0.044
C9	0.379	0.472	0.464	0.289	0.607	0.548	0.461	0.563	0.067	0.196
C10	0.309	0.351	0.354	0.226	0.473	0.418	0.341	0.431	0.154	0.056

), the causal degree, and the centrality are obtained, and the index weights are calculated from them (

Table 6. Weights of evaluation indicators.

	Impact Degree D Value	Affected Degree C Value	Centrality D-C Value	Degree of Cause D-C Value (R)	Weight
C1	3.369	3.405	6.774	−0.036	0.106
C2	3.316	4.01	7.327	−0.694	0.115
C3	2.238	3.955	6.194	−1.717	0.097
C4	3.299	2.675	5.973	0.624	0.093
C5	3.985	4.703	8.688	−0.718	0.136
C6	2.953	4.343	7.296	−1.39	0.114
C7	3.371	3.274	6.646	0.097	0.104
C8	2.26	4.247	6.506	−1.987	0.102
C9	4.046	0.648	4.694	3.398	0.073
C10	3.114	0.69	3.804	2.424	0.06

).

As can be seen in Table 5, social factors have greater weight, while natural factors have lower weight. This demonstrates that, as the concept of sustainable development gains popularity, the layout of PVCS in Qingdao is heavily influenced by service quality and public recognition. The weight of natural elements is lower because there is little variation in Qingdao’s temperature and solar resource availability. However, because solar energy resources have an important impact on photovoltaic power generation, it is essential to increase their weight when conducting research in a large area. Since photovoltaic technology is currently relatively mature, the weight of technical factors is not high. At present, the development trend of EVs is good, so its economic indicators are relatively considerable, but daily maintenance costs require careful attention, because maintenance costs are still a large cost in photovoltaic power generation [56]. Therefore, when choosing an electric vehicle PVCS site, we should pay attention to policies, public wishes, and economic indicators.

4.4. Ranking of Alternative Programs

The initial evaluation matrix was obtained according to the relevant literature and reported information, as well as the preliminary evaluation values given by experts according to Table 4. Then, clear values, period values, and language terms are converted to TFNS, and an OWA operator combines expert-provided values to produce a comprehensive TFN decision matrix P.

Among the ten sub-standards, C1, C2, C3, and C7 are cost standards, and C4, C5, C6, C8, C9, and C10 are benefit standards. The matrix P is normalized by Formula (12) to obtain a normative synthesis TFN decision matrix, as indicated in

Table 7. Standardized comprehensive TFN decision matrix.

	A1	A2	A3	A4	A5	A6	A7	A8
C1	0.89, 0.89, 0.89	1, 1, 1	0.89, 0.89, 0.89	0.62, 0.62, 0.62	0.73, 0.73, 0.73	0.32, 0.32, 0.32	0.67, 0.67, 0.67	0.89, 0.89, 0.89
C2	0.33, 0.5, 1	0.33, 0.5, 1	0.25, 0.33, 0.5	0.25, 0.33, 0.5	0.2, 0.25, 0.33	0.17, 0.2, 0.25	0.2, 0.25, 0.33	0.2, 0.25, 0.33
C3	0.33, 0.5, 1	0.33, 0.5, 1	0.33, 0.5, 1	0.2, 0.25, 0.33	0.25, 0.33, 0.5	0.17, 0.17, 0.2	0.25, 0.33, 0.5	0.25, 0.33, 0.5
C4	0, 0.167, 0.333	0.333, 0.5, 0.667	0.5, 0.667, 0.833	0.5, 0.667, 0.833	0.667, 0.833, 1	0.833, 1, 1	0.667, 0.833, 1	0.667, 0.833, 1
C5	0.167, 0.333, 0.5	0.333, 0.5, 0.667	0.5, 0.667, 0.833	0.5, 0.667, 0.833	0.667, 0.833, 1	0.833, 1, 1	0.5, 0.667, 0.833	0.667, 0.833, 1
C6	0, 0, 0.167	0.5, 0.667, 0.833	0.5, 0.667, 0.833	0.333, 0.5, 0.667	0.667, 0.833, 1	0.833, 1, 1	0.5, 0.667, 0.833	0.667, 0.833, 1
C7	0.33, 0.5, 1	0.33, 0.5, 1	0.33, 0.5, 1	0.25, 0.33, 0.5	0.2, 0.25, 0.33	0.2, 0.25, 0.33	0.25, 0.33, 0.5	0.25, 0.33, 0.5
C8	0.667, 0.833, 1	0.5, 0.667, 0.833	0.333, 0.5, 0.667	0.5, 0.667, 0.833	0.167, 0.333, 0.5	0, 0, 0.167	0.167, 0.333, 0.5	0, 0.167, 0.333
C9	0.6, 0.8, 1	0.4, 0.6, 0.8	0.4, 0.6, 0.8	0.6, 0.8, 1	0.4, 0.6, 0.8	0.4, 0.6, 0.8	0.4, 0.6, 0.8	0.4, 0.6, 0.8
C10	0.37, 0.68, 1	0.47, 0.74, 1	0.53, 0.74, 0.95	0.53, 0.74, 0.95	0.53, 0.74, 0.95	0.58, 0.74, 0.9	0.47, 0.63, 0.79	0.47, 0.63, 0.79

.

Finally, the $v_i^{\prime },d_i,u_i^{\prime }$ of each alternative can be determined by Formulations (13)–(16) and the ultimate result is reached using the ordinal dominance theory. The conclusive rankings of the alternatives are displayed in

Table 8. The ranking result by the fuzzy MULTIMOORA method.

Alternatives	${\mathit{v}}_{\mathit{i}}$	${\mathit{v}}_{\mathit{i}}^{\prime }$	Ranking	${\mathit{d}}_{\mathit{i}}$	Ranking	${\mathit{u}}_{\mathit{i}}$	${\mathit{u}}_{\mathit{i}}^{\prime }$	Ranking	Final Ranking
A1	(0.355, 0.497, 0.763)	0.528	7	0.276	5	(0, 0, 0.662)	0.165	7	7
A2	(0.452, 0.611, 0.873)	0.637	1	0.171	1	(0.421, 0.594, 0.862)	0.618	1	1
A3	(0.456, 0.601, 0.822)	0.620	2	0.195	2	(0.428, 0.580, 0.806)	0.599	2	2
A4	(0.419, 0.543, 0.689)	0.548	5	0.283	6	(0.390, 0.509, 0.657)	0.516	3	5
A5	(0.452, 0.572, 0.708)	0.576	4	0.263	4	(0.388, 0.509, 0.648)	0.514	4	4
A6	(0.440, 0.531, 0.589)	0.523	8	0.316	8	(0, 0, 0.469)	0.117	8	8
A7	(0.406, 0.526, 0.668)	0.531	6	0.303	7	(0.364, 0.487, 0.634)	0.493	5	6
A8	(0.454, 0.574, 0.716)	0.579	3	0.258	3	(0, 0.494, 0.656)	0.411	6	3

. The findings indicate that among the eight alternatives, the vicinity of Longhequan Bridge in Jimo District is the optimal location to establish a PVCS for EVs. In addition, the vicinity of Zhengyang Road in Chengyang District and the vicinity of Lijiang East Road in Huangdao District are also areas with high suitability.

5. Discussion

5.1. Comparative Analysis

We propose three methods to compare and analyze the proposed approach to verify the reliability and applicability of this model. The TOPSIS approach and the VIKOR approach are well-established methods commonly used in MCDM, and TODIM has many applications in the field of choosing a site decision-making [22,57,58]. Therefore, these three methods were selected for comparative analysis with the methods suggested in this research, and the results are displayed in Figure 9.

Evidently, the ultimate scheme ranking derived from these four methods is generally consistent. A2 is always the most suitable location area for PVCS for EVs. A2 is located near the Longquan River Bridge in Jimo District, and although it has less transportation convenience and less public recognition than areas with higher economic development levels such as Shinan District and Shibei District, the location is closer to developed areas and land price is low. In addition, the area is not yet fully developed, and the establishment of PVCS here is more likely to expand in future capacity; therefore, its suitability is the highest. The location with the least appropriateness is always A6. The main reason is that the price of land near Hong Kong Middle Road in Shinan District far exceeds other options, so the suitability of construction costs is lower and the payback period is longer. Although the traffic here is the most developed for the entire city of Qingdao, it is not enough to cover its construction costs. A1 suitability is also poor, although it is located in a relatively developed area; it is far away from other economically developed areas. If a PVCS site is set up here, the coverage area is small, and the public recognition and the service level are low. Other sites fluctuate slightly in rankings, but the overall ranking trend is basically the same. It shows that the methodology proposed in this study is robust and effective.

The various outcomes are a result of the methodology’s fundamental variances. The TOPSIS and VIKOR methods pay attention to the gap between negative and positive ideal solutions [59,60]; TODIM focuses on the variation between schemes, and the MULTIMOORA method incorporates the fuzzy weighted ratio system method, the fuzzy weighted reference point method, and the fuzzy weighted complete multiplication method through the dominance theory. The results of the comparative analysis demonstrate that the model applied in this study is dependable and applicable.

5.2. Sensitivity Analysis

Based on the vulnerability of the model to the number of experts and their different opinions on the evaluation value of the solution in the multi-criteria decision-making stage of weight determination, a dual sensitivity analysis is conducted in this paper.

5.2.1. Sensitivity Analysis of Indicator Weights

In practice, expert attitudes can vary depending on the situation. Therefore, it is necessary to conduct sensitivity analysis based on the influence of criteria weights on solar charging station site selection. The weights of the 10 evaluation criteria were fluctuated by 10% and 20% to analyze the impact of the changes in the weights of the indicators on the results of the ranking of the programs.

As can be seen from Figure 10, the ranking results of all eight options are in a stable state. There is no fluctuation in the ranking results of A2, which is the most suitable location for the solar charging station for electric vehicles. When the weight of C3 fluctuates, the sensitivity of each option is low, which is due to the larger initial investment and generally longer payback period of PV charging stations. When the weights of indicators C9 and C10 fluctuate, all scenarios show good stability, which is due to the small geographical area of this study and therefore less variation in natural criteria. Overall, most of the curves are smooth, with fewer cases of fluctuations, and the scenarios show fewer fluctuations. Therefore, the stability of the model developed in this paper can be verified by sensitivity analysis.

5.2.2. Sensitivity Analysis of the Number of Experts

Considering that the sample size may have an effect on the results, we conducted a sensitivity analysis on the number of experts. The sample sizes were set to 10, 15, 20, and 25. The results of the sensitivity analysis are shown in Figure 11.

As can be seen from the results, the ranking results of the programs change as the sample size changes. This is because the results vary with the attitude of the experts towards the available sites. With a sample size of 10, the ranking of the programs varies significantly compared to the other sample size cases. But, as the sample size increases, the results gradually become stable. Therefore, the sample size should be expanded as much as possible in the actual study.

6. Conclusions and Outlook

The effective combination of photovoltaic power generation and EV charging stations can solve the problem of carbon emissions in two directions. On one hand, it could promote the advancement of electric vehicles and reduce carbon emissions in transportation. On the other hand, photovoltaic power generation can reduce carbon emissions for traditional coal power generation. Therefore, PVCS occupy an important position in the development of EVs.

In this study, the GIS-based fuzzy DEMATEL and fuzzy MULTIMOORA methods are proposed to select PVCS sites. GIS can intuitively select the area with higher suitability, so as to make further selection. The fuzzy DEMATEL method can not only deal with the uncertainty of language evaluation effectively, but also fully consider the relationship between indicators. At the same time, the fuzzy MULTIMOORA method not only considers the uncertainty of expert evaluation, but also synthesizes three ranking methods: the ratio system method, the reference point method, and complete multiplication, which make the results more robust.

In this study, a case study of the city of Qingdao is provided to demonstrate the efficacy of the proposed method. First, GIS was used to determine eight regions with high suitability, and then the fuzzy DEMATEL and fuzzy MULTIMOORA methods were used to calculate the index weight and scheme ranking, respectively. Finally, the Jimo district near Longquan River Bridge was determined as the region with the highest suitability. At the same time, the proposed method is compared and analyzed with three other established methods and a dual sensitivity analysis is conducted to further verify its reliability and robustness.

This research offers an efficient model for site selection decision-making for PVCS, which can combine visual information technology with evaluative decision-making methods, which have strong practicability. In recent years, the Chinese government has vigorously promoted the development of the grid-connected PV market and the electric vehicle market. The model proposed in this study can reasonably select EV PV charging station sites, which helps to improve the efficiency and level of work of the government, PV power generation companies, and EV companies. For the government, the establishment of PV charging stations can promote the upgrading of energy consumption structures, the development of local industries, and carbon emission reduction. As electric vehicles have a high demand for electricity, the establishment of PV charging stations solves the problem of overproduction of electricity for PV power generation companies, reduces the requirement for energy storage equipment, and facilitates their further development. For electric vehicle companies, the charging problem is still a major problem in their industry. A reasonable location of charging stations is conducive to promoting people’s desire to buy electric vehicles, thus promoting the further development of electric vehicles. In addition, the study enriches the application areas of GIS combined with MCDM. This method can also be applied to other siting areas or the location of PVCS in other cities. However, when applying this method in future studies, attention should be paid to the size of the research region, and when the research region is small, the weight of index C9 direct normal exposure and C10 average temperature is small. However, when the study area is large, the weight of these two indicators is extremely important due to differences in geographical factors.

Although this study has made some contributions to related fields, it still has some limitations. The evaluation metric system in this study model may not be applicable to studies of PV charging station siting conducted in larger regions because of the lack of exploration of influencing factors such as politics. In future work, we may consider the influence of different evaluation scales on the weights and explore ways to quantify expert language more accurately. In the meantime, we will use other MCDM methods and consider the influence of the site size of the PV charging station built for the PV charging station siting study.