A Novel Evaluation Model of Subway Station Adaptability Based on Combination Weighting and an Improved Extension Cloud Model

Abstract

The rational selection of subway station locations is an interdisciplinary problem encompassing architecture, transportation, and other fields. Few evaluation index systems and quantitative evaluation methods exist for choosing subway station locations; thus, this paper establishes a novel evaluation framework. Overall, 21 indicators covering the construction and operation phases are selected by a literature review, providing a basis for planning decision makers. The Projection Pursuit Method (PPM) and the Bald Eagle Search (BES) algorithm are employed to assign objective weights. The Continuous Ordered Weighted Averaging (COWA) operator is utilized to obtain subjective weights. A combination weighting method is used based on game theory to improve the accuracy of weight calculation. Game theory and extension cloud theory are applied to develop an improved extension cloud model and evaluate the suitability based on optimal cloud entropy. We conduct a case study of 15 stations on the Chengdu Metro Line 11, China. The results reveal that the coordination of the development plans, the alignment with the land use plan, and regional population density are the most crucial tertiary indicators that should be considered in selecting subway station locations. These findings agree with the actual conditions, demonstrating the scientific validity of the proposed evaluation method, which outperforms classical evaluation methods. The proposed method is efficient and feasible for selecting subway station locations.

1. Introduction

The large-scale construction of high-density buildings and public transportation systems has occurred in many cities in recent decades, especially in developing countries. An appropriate and efficient public transportation system is required. Subways are an integral part of urban public transportation systems. By December 2023, there were as many as 5897 subway stations in operation in China. In March 2022, there were only 3447 subway stations in China.

However, construction accidents and unsatisfactory operational development can significantly impact the sustainable development of subways and surrounding buildings. For example, Changlingshan Station of China Wuhan Metro Line 11, which opened in 2018, is known as one of the most desolate subway stations in Wuhan. As of August 2024, the surrounding area of the subway station is very desolate, and the construction and operation are far less than expected. In April 2024, a serious safety accident occurred in subway line 10, which was under construction in Xi’an, China. The specific reasons for these problems are varied and complicated. However, from the perspective of project decision makers, the main reason for these problems is that the project planning of the subway station is not satisfactory. The social and economic development level and geological conditions around the subway station were not fully considered when planning the subway station.

The suitability of subway station locations is achieved via a process of comprehensive evaluation and the optimization of subway station locations in specific geographical environments according to various factors, such as subway system operation efficiency, passenger travel convenience, regional development goals, and sustainability. Obviously, in the planning stage of a subway project, scientifically and effectively evaluating its location suitability can effectively avoid these problems. It is worth mentioning that the adaptability evaluation of this paper mainly occurs in the planning stage of subway stations. At this stage, the primary aim is choosing the appropriate location to build and operate the subway station. The adaptability of subway stations is very complicated, and the comfort or satisfaction of passengers is considered in the design stage. That is to say, the work carried out in the design stage involves designing subway stations with various styles to meet the comfort standards and needs of passengers.

Therefore, the main research purpose of this paper is to construct an evaluation index system and evaluation model of subway station location suitability on the basis of systematic analysis of subway station location requirements in order to provide a reliable theoretical basis and practical guidance for the planning, design, and construction of subway stations.

The traditional approach to site selection involves optimizing the subway route to achieve sustainable development. These methods often focus on a certain aspect of subway line location, such as travel time [1] and the spatial distribution of the population [2]. However, selecting subway station locations is a complex decision-making problem involving various factors, e.g., economic, social, environmental, and technological factors. The traditional research approach is not suitable for selecting subway stations. Deeply understanding this complexity and constructing a multi-dimensional and comprehensive evaluation index system are important when carrying out research in this field.

The adaptability evaluation of a subway station is a typical multi-attribute evaluation problem. Most studies have used one method to determine indicator weights, which has limitations. This is not comprehensive and results in low evaluation accuracy. Therefore, we used a combination of subjective and objective weighting methods to minimize the subjectivity of expert opinion and ensure the comprehensiveness and accuracy of the evaluation results. Choosing a suitable evaluation method is crucial. The cloud correlation function of the improved extension cloud model has unique advantages when dealing with the fuzziness and randomness of the level boundary to soften the grading interval [3]. Compared with other classical methods, the cloud model can better deal with the uncertainty and complexity in the adaptation evaluation of subway stations.

Therefore, this paper develops a novel evaluation model to determine the indicator weights and assess the suitability of subway station locations. The rest of this article is arranged as follows. Section 2 summarizes the research status in this field. Section 3 constructs the evaluation index system. Section 4 shows the details of the model proposed in this paper. Section 5 presents a case analysis. Section 6 summarizes the research results and limitations of this paper.

2. Literature Review

In recent years, scholars have made some progress in research on the adaptability of subway stations; however, there are still many shortcomings and research gaps. A comprehensive and in-depth evaluation model is urgently needed to comprehensively understand and enhance the adaptability of subway stations.

The traditional approach to site selection is to optimize the subway route to achieve sustainable development. For example, Hu et al. [1] proposed a station spacing optimization model based on minimizing passengers’ travel time costs and analyzed the layout of urban metro line networks. Ahmed et al. [4] developed a comprehensive optimization model using a geographic information system (GIS) and a genetic algorithm (GA) to optimize the station location and route. Samanta et al. [5] developed a two-stage analysis model based on a GIS and GA to optimize the route. Cai et al. [2] attributed the factors affecting urban rail transit line planning to the spatial distribution of urban population during the planning period. They proposed a dynamic grid generation algorithm to predict the location of urban rail transit stations. The existing research generally lacks a multi-dimensional framework for comprehensively evaluating the adaptability of subway stations. Most studies focus on the evaluation of a single or several aspects but ignore the interaction and overall effect of subway stations as a complex system. However, selecting subway station locations is a complex decision-making problem involving various factors, e.g., economic, social, environmental, and technological factors. Optimization methods cannot handle multiple attributes, uncertainty, and the fuzzy aspects of subway station location. The uncertainty and ambiguity in the location of subway stations are due to the complex factor interactions and the uncertainty regarding future changes. For example, the uncertainty of geological conditions can significantly affect underground construction [6], and the balance between subway systems and people’s travel demand is uncertain [7]. Therefore, the traditional research approach is not suitable for selecting subway stations.

Suitability assessment has become a research hotspot in project management and engineering planning in recent years. Suitability refers to the degree to which an object is appropriate or suitable for meeting certain needs or objectives under certain conditions. Suitability assessment can be traced back to the American landscape architect McHarg, who detailed suitability assessment based on ecological planning in his book Design with Nature [8], which significantly promoted suitability assessment in urban planning. Applying this concept to site selection is critical because site selection decisions involve many factors and require a balanced consideration of various needs and objectives. Subsequently, many scholars researched the suitability of different sites for various objects. For example, Zhou et al. [9] proposed an intelligent hydrogen fueling station selection model based on fuzzy comprehensive evaluation (FCE) and neural networks. Sang [10] used the Decision-making Trial and Evaluation Laboratory (DEMATEL) and the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) to establish a framework for evaluating the suitability of electric bus locations. Asadi et al. [11] proposed a site evaluation method that combined full factorial design and the Analytic Hierarchy Process (AHP) to select wind power plant sites. Ramya et al. [12] proposed a location evaluation model based on AHP and the Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS), providing theoretical support for selecting industrial factories. Tan et al. [13] proposed an ideal matter–element extension method based on a gray clustering model for wind farm site selection and used practical examples to evaluate the method. Suitability assessment has been widely used to select sites for wind power plants, electric buses, and hydrogen refueling stations for cars. The research in these areas is relatively mature. Therefore, suitability assessment can be used to select subway station sites.

Most studies have used one method to determine the indicator weights, which has limitations, is not comprehensive, and results in low evaluation accuracy. Therefore, we used a combination of subjective and objective weighting methods to minimize the subjectivity of expert opinion and ensure the comprehensiveness and accuracy of the evaluation results. The Continuous Ordered Weighted Averaging (COWA) operator has higher flexibility and computational simplicity than traditional subjective methods. Dua et al. [14] combined COWA with Criteria Importance Through Intercriteria Correlation (CRITIC) and used a multiplicative weighting method to combine subjective and objective weights. Xing et al. [15] utilized COWA, CRITIC, and the entropy weight method (EWM) to develop a composite weighting approach incorporating subjective and objective factors. The Projection Pursuit Method (PPM) uses nonlinear equations based on the data structure and features and optimization algorithms to ascertain the indicator weight. Its computational results are realistic and reliable. Leng et al. [16] proposed an objective weight calculation method based on the improved sparrow search algorithm and the PPM. Zhang et al. [17] used a PPM based on the Particle Swarm Optimization algorithm to extract structural features from the evaluation data and obtain objective indicator weights. Selecting a subway location has multi-dimensional aspects and subjective and objective factors. Therefore, this study uses game theory and the COWA and PPM to develop a comprehensive method for determining weights that balance subjective and objective factors.

Choosing a suitable evaluation method is crucial. Traditional evaluation methods, such as TOPSIS [18], often cannot determine how many indicators are needed to achieve an objective. The gray clustering method [19] relies on the whitening weight function to determine the gray-level values, which is challenging. FCE [20] has significant subjectivity because it requires expert assessments of diverse indicators. Artificial neural networks [21] necessitate a substantial volume of sample data. It should be noted that these methods do not consider fuzziness and randomness in the hierarchical boundaries of the evaluation indicators during the assessment. The cloud correlation function of the improved extension cloud model has unique advantages in dealing with the fuzziness and randomness of the level boundary to soften the grading interval [3]. For example, Liu [22] used the improved extension cloud model to evaluate the location of liquid natural gas (LNG) ports. This method provided accurate and objective evaluation results, providing a new method for the location evaluation of LNG ports. Zou [23] proposed a safety evaluation model for ships after collisions based on the extension cloud model, demonstrating the model’s reliability. Many scholars have improved this model to adapt it to different applications. Jiang [3] proposed an improved extension cloud model based on game theory and two entropy algorithms. The empirical results showed that the results of the improved model were more accurate than those of the original one. Therefore, the improved extension cloud model is suitable for evaluating suitable locations for subway stations.

According to the above literature review, it is not difficult to find that there is an obvious research gap in the current subway station adaptability evaluation model.

(1) The current research does not seem to repeatedly consider the complexity of subway station location and lacks the research of integrating multi-dimensional evaluation indicators.

(2) Adaptability evaluation has become more and more popular, but at present, there are few research results on the suitability evaluation of subway stations; so far, no scholars have put forward a scientific evaluation model. In this study of multi-attribute evaluation, it is urgent to innovate the weight calculation method and adaptive evaluation method.

In view of these gaps, we put forward an innovative evaluation model.

The contributions of this paper are as follows: (1) In this paper, a novel evaluation index system of subway station adaptability is developed. The index system covers the construction and operation stages of subway stations, which effectively solves the complicated problem of subway station planning. It provides a reference for managers in this field. (2) Based on existing research, the objective function in the PPM is solved using the Bald Eagle Search (BES) algorithm to obtain the objective weights. Game theory and the COWA operator are used to obtain the indicator weights. This method avoids the subjectivity of expert weights in subjective weighting methods and uses an objective and science-based weight allocation approach. (3) Since the cloud model has unique advantages in dealing with the fuzziness and randomness of the level boundary, it is improved using game theory and applied to assess the suitability of subway station locations and obtain reliable and realistic evaluation results more realistic. (4) A case study is conducted on 15 subway stations of Phase I of the Chengdu Metro Line 11 in Sichuan, China. We examine the viability of the proposed evaluation method and provide a new approach for similar projects.

3. Evaluation Index System for the Suitability of Metro Station Locations

We conducted an extensive literature search on the construction and operational phases of subway stations. Considering that there is little research on the location of subway stations at present, the manuscript expands the scope of literature retrieval to the location and adaptability evaluation of engineering projects. See the last column of

Table 1. Evaluation index system for the suitability of metro station locations.

Primary Index	Secondary Index	Tertiary Index	Ref
Construction phase A	Construction cost A1	Construction Cost A11	[24,25]
		Demolition Costs A12	[26,27,28]
	Construction safety A2	Adverse Geological Conditions A21	[29,30]
		Safety Risk of Fault Areas in Construction A22	[31,32]
		Peak Ground Acceleration A23	[33,34]
		Adverse Surrounding Environmental Conditions A24	[35,36,37]
	Construction difficulty A3	Engineering Geological Conditions of Rock and Soil Mass A31	[37,38,39]
		Hydrogeological Conditions A32	[35,36,37]
		Complexity of Underground Pipelines A33	[35,40,41]
	Impact on surrounding areas A4	Impact of Construction on Traffic A41	[42,43]
		Impact of Construction on the Safety of Nearby Buildings A42	[44,45,46]
Operational phase B	Sustainable development B1	Coordination of Development Plans B11	[47,48]
		Alignment with Land Use Plan B12	[49,50]
	Operational effectiveness B2	Subway Station Passenger Flow Intensity B21	[51]
		Passenger Flow Balance B22	[52,53,54]
	Accessibility B3	Walkability to Subway Stations B31	[55]
		Transfer Convenience at Subway Hubs B32	[2]
		Road Density Near Subway Stations B33	[56,57,58]
	Development potential B4	Regional Population Density B41	[42]
		Facility Point Density B42	[59]
		Development Intensity of Land Use Types B43	[50,60,61]

for the sources of references. Then, we summarized the key factors affecting the suitability of subway station locations. We created eight categories: construction cost, construction safety, construction difficulty, impact on surrounding areas, sustainable development, operational effectiveness, accessibility, and development potential. Table 1 lists the primary, secondary, and tertiary indicators and their definitions.

3.1. Construction Cost

The construction cost of a subway station is a critical component of the total investment in a subway project. The construction cost refers to the civil engineering cost, which encompasses expenses related to earthwork, enclosure structures, supporting structures, main structures, ancillary structures, waterproofing, and other related works. The demolition costs refer to the compensation fees for relocating and constructing buildings and structures affected by the subway station project.

3.2. Construction Safety

Adverse geological conditions refer to geological processes generated by the Earth’s internal or external forces that may negatively impact practical engineering projects. These typically include collapses, landslides, debris flows, karst, ground fissures, and unique soils and rocks. The Safety Risk of Fault Areas in Construction refers to the extent of the potential impact that fault and fracture zones pose to construction safety. Peak Ground Acceleration (PGA) refers to the maximum seismic force experienced by a building during an earthquake; the higher this value, the greater the potential damage to the building. Adverse Surrounding Environmental Conditions refer to unfavorable geomorphic elements near subway stations, such as ponds, irrigation canals, rivers, and similar areas.

3.3. Construction Difficulty

The construction difficulty is directly related to the progress and quality of the project. The engineering geological conditions of the rock and soil mass affect the earthwork excavation plan, the selection of soil support structures, the grade of the foundation, and the structure’s stability in the later stages. Hydrogeological conditions determine the difficulty of the waterproofing plan for the main structure. Furthermore, it is often necessary to deal with underground pipelines at the construction site of a subway station.

3.4. Impact on Surrounding Areas

Subway stations are often located near roads with convenient transportation to facilitate passengers’ travel. The long construction period of subway stations significantly impacts the surrounding traffic. Furthermore, the excavation of foundation pits, dewatering, and drainage work cause disturbances in the rock and soil mass and change the soil moisture content, resulting in ground subsidence in adjacent areas and affecting the safety of surrounding buildings.

3.5. Sustainable Development

The coordination of development plans is required to ensure rapid construction progress and integration with the urban development plan. The higher the coordination between subway stations and urban planning, the more likely it is the project receives policy support and financial investment, improving the operation of subway stations. Additionally, an alignment with the land use plan is crucial to ensure the success of the subway station construction and the surrounding land development. The closer the subway station construction is aligned with the urban land plan, the better the subsequent development prospects for the subway stations and their environments.

3.6. Operational Effectiveness

The passenger flow intensity of the subway station has a significant influence. The higher the flow intensity, the higher the station’s operational efficiency, which is beneficial to the construction and operation of the subway station. Passenger flow balance refers to the degree of uniformity in the passenger load at a subway station in different periods and regions.

3.7. Accessibility

The walkability to the subway stations refers to the convenience of pedestrians reaching a subway station by walking. The transfer convenience at subway hubs refers to the ease of transferring within the influence area of a subway station. Road network density refers to road density in the influence area of a subway station.

3.8. Development Potential

Regional population density refers to the number of people per unit area. A high-density region has higher traffic demand and travel frequency. The facility point density refers to the number of facilities adjacent to a subway station. It includes commercial, business, financial, residential, leisure, and entertainment facilities. The denser the facility points, the more economic activities are generated, improving the development of the subway station. The development intensity of land use types refers to the regulations set by government planning departments regarding the land use type, floor area ratio, construction area, and density of the land surrounding the subway station. The higher the development intensity of land use types around the station, the higher the development potential of the surrounding area, ensuring the long-term operation of the subway.

4. Suitability Evaluation Model for Selecting Subway Station Locations

On the basis of Section 3, this section develops a novel adaptability evaluation model for selecting subway station locations. The model is mainly divided into two parts, namely, weight calculation (the following Section 4.1, Section 4.2 and Section 4.3) and evaluation grade determination (the following Section 4.4). In addition, in order to facilitate readers’ understanding, Section 4.5 of this paper explains the implementation method of this model in detail.

4.1. Subjective Weight Assignment Based on the COWA

The COWA operator for interval combinations is an improvement created by Xu et al. based on the Ordered Weighted Averaging (OWA) algorithm proposed by Yager [62]. The steps are as follows:

Step 1: Invite $n$ experts to score the indicators at the same level. They sort the data from highest to lowest and number them sequentially starting from 0, obtaining a set $H=\left(h_0,h_1,h_2,\cdots ,h_{n-1}\right)$.

Step 2: Utilize the combination number to obtain the weighted weight vector ${\alpha }_j$ [63]:

$${\alpha }_j={\displaystyle \frac{c_{n-1}^j}{{{\displaystyle \sum }}_{j=0}^{n-1}{c}_{n-1}^j}}={\displaystyle \frac{c_{n-1}^j}{2^{n-1}}},$$

(1)

where $j=0,1,\cdots ,n-1$, ${\displaystyle \sum }_{j=0}^{n-1}{\alpha }_j=1$.

Step 3: Utilize the weighted weight vector ${\alpha }_j$ to weigh the data $h_j$, resulting in the absolute weight ${\overline{\omega }}_i$ of the indicator [63]:

$${\overline{\omega }}_i={{\displaystyle \sum }}_{j=0}^{n-1}{\omega }_j\times h_j,$$

(2)

where $i=1,2,\cdots ,m$, and $m$ represents the number of indicators.

Step 4: Calculate the relative weights of the indicators [63]:

$${\omega }_i={\displaystyle \frac{{\overline{\omega }}_i}{{{\displaystyle \sum }}_{i=1}^m{\overline{\omega }}_i}}.$$

(3)

4.2. Objective Weight Assignment Based on PPM

The PPM is used to analyze the structure and characteristics of high-dimensional data, identify the optimal projection direction, and project the high-dimensional data onto a one-dimensional to three-dimensional space in the optimal projection direction. The steps are as follows [17]:

Step 1: Project high-dimensional data.

The PPM transforms the t-dimensional data $\left\{x\left(i,j\right)\mid j=1,2,\cdots ,t\right\}$ into low-dimensional projection values $z\left(i\right)$ in the projection direction defined by $a=\left\{a\left(1\right),a\left(2\right),\cdots ,a\left(t\right)\right\}$ [17]:

$$z\left(i\right)={{\displaystyle \sum }}_{i=1}^{t}a\left(j\right)x\left(i,j\right).$$

(4)

Step 2: Construct the objective function

The standard deviation and local density of the projection points are used to construct a projection index function [17]:

$$\{\begin{array}{l}maxQ\left(a\right)=S_z{D}_z\hfill \\ S_z=\sqrt{{\displaystyle \sum }_{i=1}^m\left(z\left(i\right)-{\displaystyle \frac{E(z{)}^2}{m-1}}\right)}\hfill \\ D_z={\displaystyle \sum }_{i=1}^m{\displaystyle \sum }_{i=1}^n\left(R-r\left(i,j\right)\right)·\mu \left(R-r\left(i,j\right)\right)\hfill \end{array},$$

(5)

where $Q\left(a\right)$ is the projection index function, $S_Z$ is the standard deviation of the projection values $z\left(\mathrm{i}\right)$, $D_Z$ is the local density of the projection values $z\left(\mathrm{i}\right)$, $E\left(z\right)$ is the average of the projection values $\left\{z\left(i\right)|i=1,2,\cdots ,t\right\}$, $r\left(i,j\right)$ represents the distance between samples, $R$ is the window radius for calculating the local density, and $\mu \left(R-r\left(i,j\right)\right)$ is a unit step function.

Step 3: Solve the objective function using the BES.

The BES algorithm was proposed by Alsattar et al. [64] in 2020. This optimization algorithm simulates the three hunting stages of a bald eagle: selecting the search space when the bald eagle hunts for prey, searching for prey within the search space, and diving to capture the prey.

(1) Select the search space

Bald eagles continuously adjust their positions based on the group’s best position $P_{best}$ and the group’s average position $P_{mean}$ to find the optimal search space [64]:

$$\{\begin{array}{l}{P}_{i,new}=P_{best}+\alpha \times r\times \left(P_{mean}-P_i\right)\hfill \\ P_{mean}={\displaystyle \frac{1}{N}}{\displaystyle \sum }_{i=1}^N{P}_i\hfill \end{array},$$

(6)

where $\alpha$ is the position control parameter, and $r$ is a random number in the range of $\left(0,1\right)$.

(2) Search for prey within the search space

Bald eagles search for prey within a selected search space, and their flight follows an Archimedean spiral, which is expressed as follows [64]:

$$\{\begin{array}{l}\theta \left(i\right)=a\times \pi \times \mathrm{rand}\hfill \\ r\left(i\right)={\theta }_i+R\times \mathrm{rand}\hfill \\ xr\left(i\right)=r\left(i\right)\times \sin \left(\theta \left(i\right)\right)\hfill \\ yr\left(i\right)=r\left(i\right)\times \cos \left(\theta \left(i\right)\right)\hfill \\ x\left(i\right)={\displaystyle \frac{xr\left(i\right)}{\underset{1\le i\le N}{\max }\left(\left|xr\left(i\right)\right|\right)}}\hfill \\ y\left(i\right)={\displaystyle \frac{yr\left(i\right)}{\underset{1\le i\le N}{\max }\left(\left|yr\left(i\right)\right|\right)}}\hfill \end{array},$$

(7)

$$P_{i,new}=P_i+x\left(i\right)\times \left(P_i-P_{mean}\right)+y\left(i\right)\times \left(P_i-P_{i+1}\right),$$

(8)

where $\theta \left(i\right)$ and $r\left(i\right)$ are the polar angle and polar radius of the spiral followed by the ith individual, respectively, and $a$ and $R$ are parameters that control the spiral trajectory. The ranges are $\left(0,5\right)$ and $\left(0.5,2\right)$, respectively. $x\left(i\right)$ and $y\left(i\right)$ represent the position of the bald eagle in polar coordinates.

(3) Dive to capture the prey

All of the individuals in the bald eagle population move closer to the optimal position during this phase. The trajectory of this movement is represented by the following equation [64]:

$$\{\begin{array}{l}\theta \left(i\right)=a\times \pi \times \mathrm{rand}\hfill \\ r1\left(i\right)=\theta \left(i\right)\hfill \\ xr\left(i\right)=r\left(i\right)\times \sinh \left(\theta \left(i\right)\right)\hfill \\ yr\left(i\right)=r\left(i\right)\times \cosh \left(\theta \left(i\right)\right)\hfill \\ x1\left(i\right)={\displaystyle \frac{xr\left(i\right)}{\underset{1\le i\le N}{\max }\left(\left|xr\left(i\right)\right|\right)}}\hfill \\ y1\left(i\right)={\displaystyle \frac{yr\left(i\right)}{\underset{1\le i\le N}{\max }\left(\left|yr\left(i\right)\right|\right)}}\hfill \end{array},$$

(9)

$$P_{i,new}=\mathrm{rand}\times P_{best}+x1\left(i\right)\times \left(P_i-c1\times P_{mean}\right)+y1\left(i\right)\times \left(P_i-c2\times P_{best}\right),$$

(10)

where $\sinh$ and $\cosh$ denote the hyperbolic sine and hyperbolic cosine functions, respectively. $c1$ and $c2$ represent the rates of the bald eagle’s movement toward the optimal point and the central point, respectively, with values in the range of $\left(1,2\right)$.

Equation (5) is the fitness function of the BES algorithm. The optimal solution $a^{\ast }$ is obtained through Equations (6)–(10). Subsequently, the objective weight vector $T=\left(T_1,T_2,\cdots ,T_n\right)$ is derived by squaring each element of the optimal solution $a^{\ast }$.

4.3. Combination Weighting Based on Game Theory

The game theory is utilized to combine the two weighting methods. The steps are as follows:

(1) Perform a linear combination of $N$ weight calculation methods to obtain the combined indicator weight $W$ [65]:

$$W={{\displaystyle \sum }}_{i=1}^N{\lambda }_i\times W_i,$$

(11)

where ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_N$ are the combination coefficients corresponding to different weight methods.

(2) Based on game theory, an objective function is established to minimize the sum of deviations between the combined weight W and the individual weights $W_1$, $W_2$, …, $W_N$ [65]:

$$\min \left({{\displaystyle \sum }}_{j=1}^N\parallel {{\displaystyle \sum }}_{i=1}^N{\lambda }_i\times W_i-W_j{\parallel }_2\right).$$

(12)

(3) Utilize matrix differentiation to determine the first-order derivative of the objective function to achieve its minimum value [65]:

$$\left(\begin{array}{cccc}{W}_1{W}_1^T& W_1{W}_2^T& \cdots & W_1{W}_N^T\\ W_2{W}_1^T& W_2{W}_2^T& \cdots & W_2{W}_N^T\\ ⋮& ⋮& ⋮& ⋮\\ W_N{W}_1^T& W_N{W}_2^T& \cdots & W_N{W}_N^T\end{array}\right)\left(\begin{array}{c}{\lambda }_1\\ {\lambda }_2\\ ⋮\\ {\lambda }_N\end{array}\right)=\left(\begin{array}{c}{W}_1{W}_1^T\\ W_2{W}_2^T\\ ⋮\\ W_N{W}_N^T\end{array}\right).$$

(13)

(4) After obtaining the coefficients ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_N$ from the previous equation, the coefficients are normalized to obtain the optimal weight vector $W^{\ast }$ [65]:

$$\{\begin{array}{c}{\lambda }_1^{\ast }={\displaystyle \frac{\left|{\lambda }_1\right|}{{{\displaystyle \sum }}_{i=1}^N\left|{\lambda }_i\right|}}\\ {\lambda }_2^{\ast }={\displaystyle \frac{\left|{\lambda }_2\right|}{{{\displaystyle \sum }}_{i=1}^N\left|{\lambda }_i\right|}}\\ ⋮\\ {\lambda }_N^{\ast }={\displaystyle \frac{\left|{\lambda }_N\right|}{{{\displaystyle \sum }}_{i=1}^N\left|{\lambda }_i\right|}}\\ W^{\ast }={\displaystyle \sum }_{i=1}^N{\lambda }_i^{\ast }{W}_i\end{array}.$$

(14)

4.4. Determining Evaluation Levels Based on the Improved Extension Cloud Model

The extension cloud model combines the extension theory of the matter–element with the cloud model and utilizes the characteristic parameters $E$x, En, and He from the cloud model to replace the characteristic value V in the extension model of the matter–element. This approach compensates for the shortcomings of the extension model of the matter–element in addressing uncertainties in characteristic values. Its expression is as follows:

$$R=\left[\begin{array}{ccc}N& C_1& \left(E{x}_1,E{n}_1,H{e}_1\right)\\ N& C_2& \left(E{x}_2,E{n}_2,H{e}_2\right)\\ ⋮& ⋮& ⋮\\ N& C_n& \left(E{x}_n,E{n}_n,H{e}_n\right)\end{array}\right],$$

(15)

where $R$ denotes the evaluation level, $C_n$ represents the nth evaluation index, and $\left(E{x}_n,E{n}_n,H{e}_n\right)$ are the cloud characteristic values of the index for that level.

The steps are as follows:

(1) Determine the level boundaries for the evaluation indicators.

(2) Calculate the cloud correlation degree of the indicators. This step is critical in determining the final evaluation level. The calculation formula is as follows [3]:

$${\mu }_{ij}=\exp \left(-{\displaystyle \frac{{\left(x-Ex\right)}^2}{2{\left(E_n^{\prime }\right)}^2}}\right),$$

(16)

where $x$ is the indicator value of the evaluation object, $E_n^{\prime }$ is a normally distributed random number generated with $En$ as the expected value and $He$ as the standard deviation, and $Ex$ represents the expected value corresponding to different levels of the evaluation indicator.

Two methods are typically used to calculate cloud entropy, $E_n$. The first is the “$3E_n$” entropy algorithm, which is based on the $3E_n$ rule of cloud theory. This method ignores cloud droplets outside of the interval $\left(Ex-3En, Ex+3En\right)$. It provides discrete boundaries between levels. The second is the “50% correlation degree” entropy algorithm. This method provides fuzzy boundaries between levels. The equations for both algorithms can be found in Reference [3]. Different methods to obtain the index cloud correlation degree may result in different final evaluation levels. The following strategy is used to improve the reliability of the calculation results. The correlation degrees for m (m = s × t, where s is the number of indicators, and t is the number of levels) levels are obtained using the two methods, which are denoted as $u_a=\left({\mu }_{a1},{\mu }_{a1}\cdots ,{\mu }_{am}\right)$ and ${\mu }_b=\left({\mu }_{b1},{\mu }_{b1}\cdots ,{\mu }_{bm}\right)$. Game theory is used to combine the cloud correlation degrees obtained from the two cloud entropy calculations. Equations (14)–(17) are used. The final cloud correlation degree of the index is obtained using Equation (17).

$$U=a_1·{\mu }_a+a_2·{\mu }_b,$$

(17)

where $a_1$ and $a_2$ denote the combination coefficients corresponding to different cloud entropy calculation rules, respectively.

(3) Rearrange the vector $U$ to obtain the final matrix $Z$ with the cloud correlation degree [3]:

$$Z=\left[\begin{array}{ccccc}{z}_{11}& z_{12}& z_{13}& \cdots & z_{1t}\\ z_{21}& z_{22}& z_{23}& \cdots & z_{2t}\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ z_{s1}& z_{s2}& z_{s3}& \cdots & z_{st}\end{array}\right].$$

(18)

(4) Determine the evaluation level. We multiply the combined weights $W$ with the cloud correlation degree matrix $Z$ to obtain the evaluation vector $R$ for the target. The evaluation level is derived based on the maximum membership degree [3]:

$$R=W\times Z.$$

(19)

The weighted average of the evaluation eigenvalues $K$ is obtained to compare the suitability of different subway stations [3]:

$$K={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^5(r_i\times l_j)}{{{\displaystyle \sum }}_{i=1}^5{r}_i}},$$

(20)

where $r_i$ is the component of the evaluation vector $R$, and $l_j=j\left(j=1~5\right)$ corresponds to the evaluation levels.

4.5. Implementation of the Proposed Model

A model to evaluate the suitability of subway station locations is constructed based on the indicatory system. Establishing this model consists of four parts:

(1) Calculate the subjective weights based on the COWA operator. Firstly, the experts’ judgment on the importance of indicators is obtained via a questionnaire survey or expert interview, and $H$ is obtained by sorting. Then, according to the number of experts, the expert weight ${\alpha }_j$ is calculated using Equation (1). Then, by bringing $H$ and ${\alpha }_j$ into Equation (2), the normalized index weight ${\overline{\omega }}_i$ can be obtained. Finally, the normalized subjective weight ${\omega }_i$ can be obtained by bringing ${\overline{\omega }}_i$ into Equation (3).

(2) Calculate the objective weights using the PPM optimized by the BES. Firstly, the evaluation data $x\left(i,j\right)$ are collected via various methods, and then $x\left(i,j\right)$ is brought into Equations (4) and (5) in turn to form the objective function $maxQ\left(a\right)$. Then, set the various calculation parameters of BES. Finally, the optimal projection direction $a^{\ast }$ is obtained via program calculation, and the objective weight $T$ is further obtained.

(3) Combine the weights based on game theory. Bring the calculated subjective weight and objective weight into Equation (12) to construct the objective function of game theory. By solving the objective function with Equations (13) and (14), the combined weights for subsequent evaluation can be obtained.

(4) Optimize the cloud correlation degree of the evaluation indicators in the extension cloud model based on game theory. Game theory is used to optimize the cloud correlation degree of the evaluation indicators in the extension cloud Equations (16)–(18) that are used to determine the cloud correlation degree matrix. Equation (19) is utilized to derive the comprehensive evaluation vector, and Equation (20) is used to obtain the evaluation eigenvalues for different subway station sites.

The flowchart of the model evaluation is shown in Figure 1.

It is worth mentioning that the proposed model is an adaptive evaluation model based on the PPM. From the calculation principle of the PPM, the model mainly has higher requirements or restrictions on input data. PPM obtains evaluation results by mining data structure characteristics, so missing data or more abnormal data could seriously affect the calculation performance of the model. In addition, the PPM is more effective when dealing with data sets containing enough samples. Larger data sets could provide richer information and help the model better capture and describe the internal structure of data. In the case of insufficient sample size, the model might be over-fitted; that is, the model is over-adapted to the training data and does not have good generalization ability. This is why this paper randomly extracts multiple sets of data in the preset evaluation level to ensure that the projection pursuit model has good generalization ability. From the perspective of adaptability evaluation, it is the key to ensure the success of the model to select a suitable index system and obtain accurate index data.

5. Case Study

This section is the case analysis part of the manuscript, which mainly applies the index system (Section 3 and evaluation method (Section 4) constructed in this paper to China Chengdu Metro Line 11. On the one hand, it draws a conclusion with engineering guiding value, on the other hand, it verifies the scientific and effective index system and evaluation method proposed in this paper.

5.1. Project Overview and Data Sources

We selected 15 subway station projects from the first phase of the Chengdu Metro Line 11 in China. This project involves multiple stations that are constructed using the cut-and-cover method, with excavation depths exceeding 19 m. These stations are located in suburban rural areas, development zones, core urban areas, and central business districts (CBDs) under construction. These regions exhibit significant differences in land development intensity, floor area ratio, land use types, and road planning. Additionally, the terrain of the Chengdu Metro Line 11 project includes first-grade terraces and low hills. The groundwater in the entire route of the project comprises perched water, Quaternary pore water, and bedrock fissure water. The project area receives abundant annual precipitation, with an average annual rainfall of 879.3 mm, a maximum annual rainfall of 1343.3 mm, 141 rainy days per year, and a maximum daily rainfall of 167.6 mm. The majority of precipitation (84.1%) falls from May to September.

We used quantitative and qualitative indicators. The data for the former were obtained from questionnaires completed by experts with long-term experience in municipal engineering construction. The information on the experts who participated in the questionnaire survey is listed in

Table 2. Information on experts.

No.	Work Unit	Education	Work Experience	Participated in This Project
(1)	Scientific unit	PhD	11	Yes
(2)	Construction unit	Master’s degree	8	No
(3)	Design unit	Bachelor’s degree	15	Yes
(4)	Government	Bachelor’s degree	18	Yes
(5)	Scientific unit	Associate’s degree	20	Yes
(6)	Scientific unit	Associate’s degree	14	No
(7)	Scientific unit	Associate’s degree	8	Yes
(8)	Construction unit	Associate’s degree	15	Yes
(9)	Construction unit	Associate’s degree	10	Yes
(10)	Construction unit	Master’s degree	6	Yes
(11)	Construction unit	Master’s degree	4	Yes
(12)	Construction unit	Master’s degree	12	Yes
(13)	Construction unit	Bachelor’s degree	16	Yes
(14)	Design unit	Bachelor’s degree	12	Yes
(15)	Design unit	Bachelor’s degree	15	No
(16)	Design unit	Bachelor’s degree	7	No
(17)	Design unit	Bachelor’s degree	19	Yes
(18)	Government	Bachelor’s degree	12	Yes
(19)	Government	PhD	17	Yes
(20)	Scientific unit	PhD	6	Yes

. The quantitative indicators were obtained from field investigations. The details are listed in

Table 3. Quantitative evaluation indicators.

Index	Huilong West Station	Huilong Station	Diaoyuzui Station	Lujiaocun Station	Guobin Avenue Station	Tianfu CBD East Station	Tianfu CBD North Station	Miaoeryan Station
A11	1.12	1.18	1.13	1.11	1.11	1.19	1.12	1.12
A12	0.1322	0.1655	0.3544	0.9306	0.107	0.2076	0.2390	0.1293
A21	29	23.5	11	53.5	53	29.5	17	46.5
A22	6792	5496	3358	1558	361	1333	1023	886
A23	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
A24	93	8	88	75.5	31	15	84.5	52.5
A31	52	53	57	65	75	77	81	75
A32	61	81	67	71	78	76	70	79
A33	14	15	11	4	20	79	77	39
A41	4	40	10	29	0	27	21	4
A42	0	0	0	0	0	0	7	0
B11	12	53	34	48	58	98	96	95
B12	0.88	0.49	0.77	0.78	0.82	0.91	0.73	0.71
B21	1258	6120	1483	4856	3363	14,562	15,256	10,765
B22	1.2	1.4	1.3	1.5	1.4	1.7	1.8	2
B31	1.44	1.41	1.27	1.32	1.24	1.17	1.19	1.31
B32	1	9	1	6	0	2	4	4
B33	1.24	6.73	3.45	4.55	4.78	15.12	16.32	6.44
B41	539	321	660	954	832	1642	1642	2198
B42	1.27	25.46	3.82	56.02	3.82	47.11	154.06	50.93
B43	1.53	2.17	2.33	2.92	2.67	2.72	2.51	1.91
Index	Shenyang Road Station	Lushan Avenue Station	Wanan Station	Xinchuan Tech Park South Station		Xinchuan Tech Park East Station	Xinchuan Tech Park Station	Huilong Avenue Station
A11	1.1	1.13	1.12	1.12		1.1	1.1	1.11
A12	0.4229	0.1985	0.1293	0.1090		0.3987	0.1673	0.2489
A21	22	23	21	35		20	37	30.5
A22	362	305	1246	1726		1836	2201	2720
A23	0.1	0.1	0.1	0.1		0.1	0.1	0.1
A24	55	12	54.5	13		69	76.5	87
A31	68	73	71	80		77	74	83
A32	77	89	73	81		67	82	87
A33	42	82	13	22		22	26	52
A41	63	72	16	27		42	39	32
A42	28	83	0	0		0	0	0
B11	82	83	48	56		68	63	83
B12	0.89	0.8	0.76	0.74		0.76	0.74	0.73
B21	13,435	14,560	9966	4265		3567	5578	10,568
B22	1.9	2.1	1.4	1.4		1.3	1.5	1.4
B31	1.26	1.22	1.23	1.32		1.28	1.29	1.27
B32	5	14	0	1		1	3	9
B33	5.91	9.27	5.27	12.53		7.4	13.21	13.63
B41	11,848	21,656	8802	648		1000	4104	7208
B42	91.67	189.71	44.56	3.82		21.65	3.82	31.83
B43	2.03	2.31	2.39	2.35		2.34	2.21	2.62

.

In this paper, the arithmetic average of 20 experts’ scores on an index is taken as the score of this qualitative index. The questionnaire survey results have passed the Cronbach’s alpha test, so we think the evaluation results are effective.

The calculation methods of some indicators shown in Table 3 are as follows. In this paper, the data of B₁₂ are represented by the ratio of the overlapping area of the subway station and the corresponding land and the actual area of the subway station. Therefore, the calculation formula of B₁₂ is

$$B_{12}=S_1/S_2,$$

(21)

where $S_1$ is the overlapping area between the subway station and the corresponding land, $S_2$ is the actual floor area of the subway station. The data are mainly obtained by querying the urban master plan and subway station construction drawings issued by the Planning and Natural Resources Administration.

This paper uses the following methods to calculate the data of B₂₁:

$$B_{21}=a/p,$$

(22)

where $a$ is the daily average passenger flow of the station, and $p$ is the design scale of the total station of the line. The data can be obtained by consulting the passenger flow data published on the local subway official website and the line design scale data published on the local official website.

This paper uses the following methods to calculate the data of B₂₂:

$$B_{22}=c/l,$$

(23)

where $c$ is the full-day two-way maximum cross-section passenger flow of the site, and $l$ is the average passenger flow of the site section. The data are obtained by consulting the passenger flow forecast report and the passenger flow data published on the official website of the local subway.

In this study, the detour coefficient is used to represent the accessibility of walking. The detour coefficient is the ratio of the actual travel distance to the straight-line distance. The smaller the detour coefficient, the more convenient it is to reach the station. The calculation formula of B₃₁ is

$$B_{31}=L_W/L,$$

(24)

where $L_W$ is the average of the shortest distances from the subway station to eight directions, $L$ is the straight-line distance, and 500 m is taken as the example analysis in this paper. The data needed for this indicator are obtained through satellite maps.

This paper uses the following methods to calculate the data of B₃₃:

$$B_{33}=L_{33}/S,$$

(25)

where $L_{33}$ is the sum of all road lengths in the neighborhood of the station, and $S$ is the neighborhood area of the station. Data related to this indicator are obtained through a Gaode map and a Baidu map.

This paper obtains the population density of each site according to the population density and area ratio of each community within the service scope of the site. Therefore, the calculation formula of B₄₁ is:

$$B_{41}={{\displaystyle \sum }}_{k=1}^n{\alpha }_k{\beta }_k,$$

(26)

where ${\alpha }_k$ is the proportion of the area occupied by community $k$ within the service scope, ${\beta }_k$ is the population density of community $k$, and $n$ is the number of communities within the service scope. The data of this index are obtained by querying the local city government service network and administrative division map.

This paper uses the following methods to calculate the data of B₄₂:

$$B_{42}=e/f,$$

(27)

where $e$ is the annual gross regional GDP, and $f$ is the population of the region. The data are obtained through the government official website and regional yearbooks. It should be noted that at present, the smallest units of statistical GDP are districts and counties.

5.2. Determining the Weights of Evaluation Indexs

Due to space limitations, we use the Diaoyuzui Station as an example. The subjective weights were calculated using Equations (1)–(3). The PPM, MATLAB 2016a, and Equations (4)–(10) were used to determine the optimal projection direction and objective weights. Game theory was used to calculate the undetermined coefficients ${\lambda }_1=0.44$ and ${\lambda }_2=0.56$ using Equations (11)–(14). The comprehensive weight vector $W$ was obtained (

Table 4. Weights of evaluation indicators.

Primary Index	Comprehensive Weight	Secondary Index	Relative Weight	Comprehensive Weight	Third-Level Index	Relative Weight	Comprehensive Weight
A	0.5277	A1	0.1182	0.0624	A11	0.3679	0.0229
					A12	0.6321	0.0394
		A2	0.3750	0.1979	A21	0.2894	0.0573
					A22	0.2018	0.0399
					A23	0.2679	0.0530
					A24	0.2409	0.0477
		A3	0.2993	0.1580	A31	0.3528	0.0557
					A32	0.3477	0.0549
					A33	0.2995	0.0473
		A4	0.2075	0.1095	A41	0.5040	0.0552
					A42	0.4960	0.0543
B	0.4723	B1	0.2631	0.1242	B11	0.5087	0.0632
					B12	0.4913	0.0610
		B2	0.1706	0.0806	B21	0.6919	0.0558
					B22	0.3081	0.0248
		B3	0.2132	0.1007	B31	0.2419	0.0244
					B32	0.3924	0.0395
					B33	0.3657	0.0368
		B4	0.3531	0.1667	B41	0.3487	0.0581
					B42	0.3117	0.0520
					B43	0.3396	0.0566

).

5.3. Determining the Evaluation Level

We utilized the Chinese standards for urban rail transit, including the Code for the Seismic Design of Urban Rail Transit Structures (GB50909-2014), the Code for Engineering Geological Investigation of Urban and Rural Planning (CJJ57-2012), and the Code for Investigation of Geotechnical Engineering of Urban Rail Transit (GB50307-2012) to classify the suitability of subway locations into five levels: highly suitable (I), suitable (II), relatively suitable (III), relatively unsuitable (IV), and unsuitable (V). The classification criteria for the quantitative and qualitative indicators are summarized in

Table 5. Classification criteria for the evaluation index levels.

Index	Unit	I	II	III	IV	V
A11	10K RMB/m2	[0,0.57)	[0.57,1.14)	[1.14,1.71)	[1.71,2.28)	[2.28,$+\infty$)
A12	100M RBM	[0,0.4)	[0.4,0.8)	[0.8,1.2)	[1.2,1.6)	[1.6,$+\infty$)
A21	-	[0,20)	[20,40)	[40,60)	[60,80)	[80,100]
A22	m	[1100,$+\infty$)	[800,1100)	[500,800)	[200,500)	[0,200)
A23	g	[0,0.05)	[0.05,0.1)	[0.1,0.2)	[0.2,0.3)	[0.3,0.4)
A24	-	[0,20)	[20,40)	[40,60)	[60,80)	[80,100]
A31	-	[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
A32	-	[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
A33	-	[0,20)	[20,40)	[40,60)	[60,80)	[80,100]
A41	-	[0,20)	[20,40)	[40,60)	[60,80)	[80,100]
A42	-	[0,20)	[20,40)	[40,60)	[60,80)	[80,100]
B11	-	[80,100]	[60,80)	[40,60)	[20,40)	[0,20)
B12	%	[0.8,1]	[0.6,0.8)	[0.4,0.6)	[0.2,0.4)	[0,0.2]
B21	person-days	[17,600,$+\infty$)	[132,00,17,600)	[8800,13,200)	[4400,8800)	[0,4400)
B22	-	[1,1.5)	[1.5,2.0)	[2.0,2.5)	[2.5,3.0)	[3.5,$+\infty$)
B31	-	[1,1.3)	[1.3,1.6)	[1.6,1.9)	[1.9,2.1)	[2.1,$+\infty$)
B32	-	[20,$+\infty$)	[15,20)	[10,15)	[5,10)	[0,5)
B33	Km/km2	[12,$+\infty$)	[9,12)	[6,9)	[3,6)	[0,3)
B41	pop/km2	[5500,$+\infty$)	[4000,5500)	[2500,4000)	[1000,2500)	[0,1000)
B42	units/km2	[450,$+\infty$)	[250,450)	[100,250)	[30,100)	[0,30)
B43	-	[4.0,$+\infty$)	[3.5,4.0)	[2.0,3.5)	[1.5,2.0)	[0,1.5)

.

We used the classification criteria and the cloud entropy equation from reference [22] and developed two cloud models to assess the suitability levels of subway station locations. The results are presented in

Table 6. 3En entropy extension cloud model.

Index	I	II	III	IV	V
A11	(0.285,0.095,0.001)	(0.855,0.095,0.001)	(1.425,0.095,0.001)	(1.995,0.095,0.001)	(2.565,0.095,0.001)
A12	(0.2,0.067,0.001)	(0.6,0.067,0.001)	(1,0.067,0.001)	(1.4,0.067,0.001)	(1.8,0.067,0.001)
A21	(10,3.33,0.001)	(30,3.33,0.001)	(50,3.33,0.001)	(70,3.33,0.001)	(90,3.33,0.001)
A22	(6050,1650,0.001)	(950,50,0.001)	(650,50,0.001)	(350,50,0.001)	(100,33.33,0.001)
A23	(0.025,0.008,0.001)	(0.075,0.008,0.001)	(0.15,0.017,0.001)	(0.25,0.017,0.001)	(0.35,0.017,0.001)
A24	(10,3.33,0.001)	(30,3.33,0.001)	(50,3.33,0.001)	(70,3.33,0.001)	(90,3.33,0.001)
A31	(90,3.33,0.001)	(70,3.33,0.001)	(50,3.33,0.001)	(30,3.33,0.001)	(10,3.33,0.001)
A32	(90,3.33,0.001)	(70,3.33,0.001)	(50,3.33,0.001)	(30,3.33,0.001)	(10,3.33,0.001)
A33	(10,3.33,0.001)	(30,3.33,0.001)	(50,3.33,0.001)	(70,3.33,0.001)	(90,3.33,0.001)
A41	(10,3.33,0.001)	(30,3.33,0.001)	(50,3.33,0.001)	(70,3.33,0.001)	(90,3.33,0.001)
A42	(10,3.33,0.001)	(30,3.33,0.001)	(50,3.33,0.001)	(70,3.33,0.001)	(90,3.33,0.001)
B11	(90,3.33,0.001)	(70,3.33,0.001)	(50,3.33,0.001)	(30,3.33,0.001)	(10,3.33,0.001)
B12	(0.9,0.033,0.001)	(0.7,0.033,0.001)	(0.5,0.033,0.001)	(0.3,0.033,0.001)	(0.1,0.033,0.001)
B21	(19,800,733.33,0.001)	(15,400,733.33,0.001)	(11,000,733.33,0.001)	(6600,733.33,0.001)	(2200,733.33,0.001)
B22	(1.25,0.083,0.001)	(1.75,0.083,0.001)	(2.25,0.083,0.001)	(2.75,0.083,0.001)	(3.75,0.083,0.001)
B31	(1.15,0.05,0.001)	(1.45,0.05,0.001)	(1.75,0.05,0.001)	(2,0.033,0.001)	(2.25,0.05,0.001)
B32	(22.5,0.833,0.001)	(17.5,0.833,0.001)	(12.5,0.833,0.001)	(7.5,0.833,0.001)	(2.5,0.833,0.001)
B33	(13.5,0.5,0.001)	(10.5,0.5,0.001)	(7.5,0.5,0.001)	(4.5,0.5,0.001)	(1.5,0.5,0.001)
B41	(30,250,24,750,0.001)	(4750,250,0.001)	(3250,250,0.001)	(1750,250,0.001)	(500,167,0.001)
B42	(550,33.33,0.001)	(350,33.33,0.001)	(175,25,0.001)	(65,11.67,0.001)	(15,5,0.001)
B43	(4.75,0.25,0.001)	(3.75,0.083,0.001)	(2.75,0.25,0.001)	(1.75,0.083,0.001)	(0.75,0.25,0.001)

and

Table 7. Extension cloud model with 50% correlation degree.

Index	I	II	III	IV	V
A11	(0.285,0.242,0.001)	(0.855,0.242,0.001)	(1.425,0.242,0.001)	(1.995,0.242,0.001)	(2.28,0.242,0.001)
A12	(0.2,0.17,0.001)	(0.6,0.17,0.001)	(1,0.17,0.001)	(1.4,0.17,0.001)	(1.8,0.17,0.001)
A21	(10,8.493,0.001)	(30,8.493,0.001)	(50,8.493,0.001)	(70,8.493,0.001)	(90,8.493,0.001)
A22	(6050,4204.18,0.001)	(950,127.4,0.001)	(650,127.4,0.001)	(350,127.4,0.001)	(100,84.9,0.001)
A23	(0.025,0.021,0.001)	(0.075,0.021,0.001)	(0.15,0.042,0.001)	(0.25,0.042,0.001)	(0.35,0.042,0.001)
A24	(10,8.493,0.001)	(30,8.493,0.001)	(50,8.493,0.001)	(70,8.493,0.001)	(90,8.493,0.001)
A31	(90,8.493,0.001)	(70,8.493,0.001)	(50,8.493,0.001)	(30,8.493,0.001)	(10,8.493,0.001)
A32	(90,8.493,0.001)	(70,8.493,0.001)	(50,8.493,0.001)	(30,8.493,0.001)	(10,8.493,0.001)
A33	(10,8.493,0.001)	(30,8.493,0.001)	(50,8.493,0.001)	(70,8.493,0.001)	(90,8.493,0.001)
A41	(10,8.493,0.001)	(30,8.493,0.001)	(50,8.493,0.001)	(70,8.493,0.001)	(90,8.493,0.001)
A42	(10,8.493,0.001)	(30,8.493,0.001)	(50,8.493,0.001)	(70,8.493,0.001)	(90,8.493,0.001)
B11	(90,8.493,0.001)	(70,8.493,0.001)	(50,8.493,0.001)	(30,8.493,0.001)	(10,8.493,0.001)
B12	(0.9,0.085,0.001)	(0.7,0.085,0.001)	(0.5,0.085,0.001)	(0.3,0.085,0.001)	(0.1,0.085,0.001)
B21	(19,800,1858.5,0.001)	(15,400,1868.5,0.001)	(11,000,1868.5,0.001)	(6600,1868.5,0.001)	(2200,1868.5,0.001)
B22	(1.25,0.085,0.001)	(1.75,0.085,0.001)	(2.25,0.085,0.001)	(2.75,0.085,0.001)	(3.75,0.085,0.001)
B31	(1.15,0.127,0.001)	(1.45,0.127,0.001)	(1.75,0.127,0.001)	(2,0.085,0.001)	(2.25,0.127,0.001)
B32	(22.5,2.123,0.001)	(17.5,2.123,0.001)	(12.5,2.123,0.001)	(7.5,2.123,0.001)	(2.5,2.123,0.001)
B33	(13.5,1.274,0.001)	(10.5,1.274,0.001)	(7.5,1.274,0.001)	(4.5,1.274,0.001)	(1.5,1.274,0.001)
B41	(30,250,21,020.9,0.001)	(4750,637,0.001)	(3250,637,0.001)	(1750,637,0.001)	(500,425,0.001)
B42	(550,85,0.001)	(350,85,0.001)	(175,63.7,0.001)	(65,29.7,0.001)	(15,12.7,0.001)
B43	(4.75,0.637,0.001)	(3.75,0.212,0.001)	(2.75,0.637,0.001)	(1.75,0.212,0.001)	(0.75,0.637,0.001)

.

We input the expected value ($Ex$), entropy ($En$), super-entropy ($He$), indicator values, and weight vectors into MATLAB and obtained the model solution. We calculated the cloud correlation degree 1000 times and used the median of the results as the cloud correlation degree of the evaluation indicators. The final cloud correlation degree matrix and evaluation vector were derived based on game theory. The results are listed in

Table 8. Cloud correlation degree matrix for Diaoyuzui Station.

Third-Level Index	I	II	III	IV	V	Evaluation Result
A11	0.0018	0.4282	0.3874	0.0014	0.0000	Suitable
A12	0.5499	0.2854	0.0006	0.0000	0.0000	Very suitable
A21	0.9861	0.0664	0.0000	0.0000	0.0000	Very suitable
A22	0.3684	0.0000	0.0000	0.0000	0.0000	Very suitable
A23	0.0016	0.4069	0.4083	0.0016	0.0000	Suitable
A24	0.0000	0.0000	0.0000	0.0858	0.9466	Unsuitable
A31	0.0004	0.2514	0.5980	0.0052	0.0000	Relatively suitable
A32	0.0207	0.8878	0.1094	0.0001	0.0000	Suitable
A33	0.9861	0.0664	0.0000	0.0000	0.0000	Very suitable
A41	1.0000	0.0507	0.0000	0.0000	0.0000	Very suitable
A42	0.4074	0.0016	0.0000	0.0000	0.0000	Very suitable
B11	0.0000	0.0001	0.1375	0.8176	0.0150	Relatively unsuitable
B12	0.2513	0.5973	0.0051	0.0000	0.0000	Suitable
B21	0.0000	0.0000	0.0000	0.0190	0.8704	Suitable
B22	0.9464	0.0857	0.0000	0.0000	0.0000	Very suitable
B31	0.5308	0.2993	0.0007	0.0000	0.0000	Very suitable
B32	0.0000	0.0000	0.0000	0.0075	0.6686	Unsuitable
B33	0.0000	0.0000	0.0052	0.5981	0.2514	Relatively unsuitable
B41	0.4670	0.0000	0.0000	0.0439	0.6887	Unsuitable
B42	0.0000	0.0002	0.0227	0.1013	0.5756	Unsuitable
B43	0.0006	0.0000	0.6985	0.0194	0.0374	Relatively suitable

and

Table 9. Evaluation results for the stations.

Site	I	II	III	IV	V	Suitability Level	Evaluation Eigenvalues
Huilong West Station	0.2643	0.1337	0.1009	0.0370	0.2910	Unsuitable	3.05
Huilong Station	0.2472	0.1409	0.2719	0.1076	0.0743	Relatively suitable	3.45
Diaoyuzui Station	0.2971	0.1612	0.1198	0.0885	0.2024	Very suitable	3.30
Lujiaocun Station	0.1308	0.2434	0.2482	0.1921	0.0431	Relatively suitable	3.26
Guobin Avenue Station	0.2221	0.2224	0.1807	0.1004	0.1035	Very suitable	3.43
Tianfu CBD East Station	0.2901	0.2797	0.1049	0.1123	0.0550	Very suitable	3.76
Tianfu CBD North Station	0.2696	0.3012	0.1332	0.0977	0.0700	Suitable	3.69
Miaoeryan Station	0.2209	0.2417	0.2650	0.1263	0.0376	Relatively suitable	3.54
Shenyang Road Station	0.1995	0.2928	0.1809	0.1537	0.0211	Suitable	3.58
Lushan Avenue Station	0.2911	0.2372	0.1720	0.1081	0.0596	Very suitable	3.68
Wanan Station	0.2160	0.1934	0.1918	0.0650	0.0147	Very suitable	3.77
Xinchuan Tech Park South Station	0.2244	0.2462	0.1071	0.0269	0.1138	Suitable	3.61
Xinchuan Tech Park East Station	0.1781	0.3151	0.1566	0.0841	0.1153	Suitable	3.42
Xinchuan Tech Park Station	0.2058	0.3084	0.1190	0.0849	0.0891	Suitable	3.57
Huilong Avenue Station	0.2877	0.2395	0.1948	0.0571	0.0580	Very suitable	3.78

.

5.4. Analysis of Evaluation Results

The results indicated that Diaoyuzui Station, Guobin Avenue Station, Tianfu CBD East Station, Lushan Avenue Station, Wan’an Station, and Huilong Avenue Station were highly suitable. Huilong Road Station, Lujiaocun Station, and Miaoreyan Station were relatively suitable. Tianfu CBD North Station, Shenyang Road Station, Xinchuan Tech Park South Station, Xinchuan Tech Park East Station, and Xinchuan Tech Park Station were suitable, and only Huilong West Station was unsuitable.

Huilong Avenue Station ranked the highest. It was surrounded by other projects during its construction, but there was no impact on the surrounding buildings. It also suffered the least damage among all stations of the Chengdu Metro Line 11 during the 2018 flood season. Furthermore, no buildings existed on the site of the Huilong Avenue Station, resulting in low demolition costs. All of the surrounding construction projects were completed during the station’s operation, and the surroundings and nearby residents were not affected. The construction and operational phases of this subway station did not result in any problems, which is consistent with the evaluation results.

In contrast, Huilong West Station had the lowest suitability rating. Its geotechnical and hydrogeological conditions were unfavorable; thus, it ranked fourth among the fifteen stations. Since its opening in 2020, the station’s passenger flow has remained low, reflecting the lagging development and insufficient transportation demand in the surrounding area. In summary, the site selected for Huilong West Station was inappropriate, highly consistent with our results, demonstrating the method’s rigor and accuracy.

5.5. Discussion

We compared the proposed model with traditional evaluation models. The results are listed in

Table 10. Comparison of results from different evaluation models.

Site	3En Entropy Extension Cloud Model	50% Relevance Entropy Extension Cloud Model	FCE	The Improved Extension Cloud Model
Huilong West Station	Unsuitable	Unsuitable	Relatively suitable	Unsuitable
Huilong Station	Relatively suitable	Very suitable	Suitable	Relatively suitable
Diaoyuzui Station	Very suitable	Very suitable	Very suitable	Very suitable
Lujiaocun Station	Suitable	Relatively suitable	Relatively suitable	Relatively suitable
Guobin Avenue Station	Suitable	Relatively suitable	Suitable	Very suitable
Tianfu CBD East Station	Very suitable	Very suitable	Very suitable	Very suitable
Tianfu CBD North Station	Suitable	Suitable	Suitable	Suitable
Miaoeryan Station	Relatively suitable	Relatively suitable	Suitable	Relatively suitable
Shenyang Road Station	Suitable	Very suitable	Very suitable	Suitable
Lushan Avenue Station	Very suitable	Very suitable	Very suitable	Very suitable
Wanan Station	Very suitable	Very suitable	Suitable	Very suitable
Xinchuan Tech Park South Station	Suitable	Very suitable	Suitable	Suitable
Xinchuan Tech Park East Station	Suitable	Suitable	Suitable	Suitable
Xinchuan Tech Park Station	Suitable	Suitable	Very suitable	Suitable
Huilong Avenue Station	Very suitable	Very suitable	Very suitable	Very suitable

. The suitability assessment results for the FCE are generally consistent with engineering practice, but the contrast of the evaluation results was poor. The results showed that six subway stations (Diaoyuzui Station, Tianfu CBD East Station, Shenyang Road Station, Lushan Avenue Station, Xinchuan Tech Park Station, and Huilong Avenue Station) were highly suitable. The evaluation results of the two traditional cloud models and the extension cloud models were consistent. Furthermore, the use of the eigenvalues compensated for the lack of ranking in the FCE. Additionally, the evaluation results were consistent for the three models for ten stations (Huilong Road West Station, Diaoyuzui Station, Tianfu CBD East Station, Tianfu CBD North Station, Miaoeryan Station, Lushan Avenue Station, Wan’an Station, Xinchuan Tech Park East Station, Xinchuan Science and Xinchuan Tech Park Station, and Huilong Avenue Station). The results obtained from the improved extension cloud model were consistent with those of the other two models for five stations. Thus, the improved extension cloud model could determine the evaluation levels and provide evaluation results consistent with the traditional extension cloud models. The comparison results indicate the applicability of the improved extension cloud model in evaluation assessments.

In addition, this paper compared similar research results in the world. At present, there are many research results on project site selection adaptability evaluation, which are mainly aimed at roof photovoltaic projects [66] and waste incineration power generation projects [67]. Similar to this paper, these research results proved that the method based on quantitative evaluation is scientific and effective. From the research conclusion, we all emphasized that the project site selection adaptability evaluation is a complex multi-attribute evaluation problem, which needs to consider the construction and operation of the project comprehensively. Because the research objects are quite different, the conclusions of case studies lack comparability. However, with the increase in research results relating to subway station adaptability evaluation in the future, there will be more interesting conclusions for comparison. In addition, at present, the evaluation of the applicability of subway projects mainly focuses on the adaptability evaluation of service facilities [68], the adaptability evaluation of subway station charging area [69], and the adaptability evaluation of passengers to subway microenvironment [70]. Obviously, these studies are only limited to one aspect of subway project adaptability, and they could provide detailed and valuable suggestions for a certain aspect of subway station adaptability. However, for subway project managers, especially planning managers, these research results are too detailed and lack a macroscopic and conclusive research result. Compared with these detailed research results, this paper stands in the perspective of the whole life cycle of subway stations, and the research results mainly provide services for the construction and operation of the project. Therefore, the research results of this paper are more comprehensive and practical.

6. Conclusions

This paper proposed a novel suitability evaluation model for subway site selection. Based on a literature review, this paper constructed an evaluation index system that included three levels, which covered all aspects of the construction and operation of subway stations. This provides an effective decision-making tool for the planners of subway projects. We used the BES-optimized PPM to calculate the objective indicator weights and the COWA operator to determine the subjective weights. The weights were combined using the game theory to obtain the final weights. This approach addressed the problem of using different weight calculation methods. Compared with other existing research methods, the model proposed in this paper can evaluate the adaptability of subway stations more accurately. The results of the case study indicated that most station locations were suitable or highly suitable, which agreed with the actual project conditions, demonstrating the model’s validity. Wan’an Station has the highest suitability, followed by Huilong Dadao Station, whereas Huilong Road West Station has the lowest suitability. Construction safety and development potential are the most important secondary indicators. The coordination of the development plans, alignment with land use plans, and regional population density were critical tertiary indicators of the suitability of subway station locations. Therefore, project managers should prioritize these key factors during early-stage decision-making.

The primary limitations of this study are the lack of a unified evaluation index and dynamic evaluation model. The planning of subway stations is very complicated and often changes dynamically. Therefore, a unified and universal evaluation index system and a dynamic evaluation model should be developed in this field in the future. In addition, this paper only analyzes the adaptability of subway stations from the planning stage. Diversified design, reliable construction, efficient operation team, passenger satisfaction and happiness will greatly affect the adaptability of subway stations. In the future, we should consider the adaptability of subway stations from more aspects.