# Comprehensive Evaluation Model of Coal Mine Safety under the Combination of Game Theory and TOPSIS

Authors: Hongxia Li; Lei Chen; Fangyuan Tian; Lin Zhao; Shuicheng Tian
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

At present, the frequent occurrence of coal mine accidents in China is a key concern in the field of safety. Although the coal mine accident rate is decreasing due to the progress of technology and the improvement of management, there is still a lack of comprehensive evaluation of the role of various factors in the coal mine. Therefore, the purpose of this study is to establish a game theory combination weight-TOPSIS comprehensive evaluation model based on the analysis of various factors affecting coal mine safety. The model combines the weights obtained from fuzzy analytic hierarchy process (FAHP), entropy weight method (EWM), and back propagation neural network (BP-NN) by using the combination method of game theory and then combines with the TOPSIS method to evaluate 20 indicators in four aspects of a coal mine: personnel, equipment, environment, and management. Taking five mines under Zheng Coal Group as an example, the evaluation results of the game theory combination weight-TOPSIS comprehensive evaluation model are compared with those of the fuzzy analytic hierarchy process and the improved composite weight-TOPSIS method. The results show that the safety grade of the five mine samples under Zhengmei Group is ranked as follows: mine 4 > grade II (relatively safe) > mine 2 > mine 5 > grade III (moderately safe) > mine 3 > mine 1 > grade IV (generally safe). The evaluation result of the game theory combination weight-TOPSIS method is basically consistent with the actual safety situation of the coal mine, which reflects the superiority and practicality of the evaluation model. The model has greater differentiation in the process of determining the coal mine safety grade, and the evaluation results are more intuitive and reasonable, which can provide a more effective evaluation tool for the comprehensive evaluation of coal mine safety. Finally, based on the evaluation results, corresponding policy recommendations to improve the status quo of coal mine safety are proposed, aiming to provide decision-making reference for coal mine safety management personnel.


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## Body

## 1. Introduction

Energy security is critical to the sustainable development of all countries and is high on the policy agenda of governments [1, 2]. China’s energy structure is extremely unbalanced. Two-thirds of the energy consumption is provided by coal, so coal is the essential energy source in China. As a developing country with a rapidly growing economy, the high reliance on coal makes the coal strategy a major concern for policymakers [3, 4]. According to various statistics, China is relatively rich in coal and recoverable reserves. It is the leading coal producer and has the largest number of coal mines (approximately 12,000) [5, 6]. However, the number of open-pit coal mines in China is far less than in other countries, and a large amount of coal is mined underground [7]. The environment, geological conditions, and mine scale under the mine [8] cause the difficulty and danger of coal mining, and the safety production can not be guaranteed [9]. The harsh working environment, complex working conditions, and many dangerous factors such as gas explosion, collapse, and water inrush [10–12] have resulted in China’s coal mine accident casualty rate reaching over 70% of the global rate [13], forming a more severe situation of coal mine safety production. Under the severe situation of frequent coal mine accidents, countries worldwide are aware of the current coal mine safety crisis. They have taken corresponding countermeasures to improve the current level of coal mine safety [14]. Chinese government departments have taken a series of major measures to reduce the occurrence of coal mine accidents and improve the safety level, such as “closing down coal mines with a smaller scale or poor production conditions,” “strengthening safety legislation,” and “establishing an independent coal mine safety monitoring system,”.The coal mine production system is composed of people and the environment working together, and the environment can be divided into the natural environment and derived environment. The natural environment refers to those coal mine geological conditions with natural characteristics formed by nature. The derived environment refers to the coal mining process and the design of its input elements determined by people in the production process, including equipment [15], management [16], and workplace environment [17] mentioned in the accident cause theory. Therefore, its establishment and guarantee are safe conditions that can promote the stability of the coal mine production system and reduce the probability of coal mine accidents [18]. However, the coal mine production system is a comprehensive and complex system, and various risk factors are three-dimensionally distributed in space and dynamically developed in time. The resulting coal mine accidents are characterized by ambiguity, randomness, and dynamics [19]. Frequent coal mine accidents have always been regarded as one of the most prominent problems in China. These accidents not only caused massive loss of life and property but also had a negative impact on society. It has seriously affected coal production and sustainable economic and social development [20].Therefore, to ensure the orderly and efficient operation of coal mine safety production, it is necessary to conduct a comprehensive safety evaluation of coal mines to further strengthen the mine safety infrastructure. Through the evaluation, the existing and potential risks can be identified. After determining the dangerous state of the coal mine production system, it provides early warning alerts to avoid accidents and reduce losses.This paper aims to analyze various influencing factors in four aspects of human, machine, environment, management of coal mine production system, combine several weight determination methods and use the combination weighting principle of game theory to construct the game theory combination weight-TOPSIS comprehensive evaluation model, which is applied to the evaluation of mine safety. The feasibility and rationality of the model are verified by an example, which provides a guarantee for the improvement of the coal mine safety evaluation level and technical management level. The results of this evaluation method can guide coal enterprises to design safety schemes and implement new safety strategies.


## 2. Literature Review

Safety evaluation refers to the application of relevant engineering control principles and standards to judge and analyze the potential risks and unstable factors in the project and system, calculate the possibility and damage degree of engineering and system failures and related hazards and put forward corresponding safety solutions to ensure the normal and stable operation of the project [21]. As early as the 1930s, safety evaluation techniques began to be used in the insurance industry to determine insurance rates by measuring the risk of an accident. In the 1960s, under the promotion of system safety engineering, safety evaluation techniques have been greatly developed [22]. In 1964, Dow Chemical Company of the United States conducted a safety evaluation for chemical production and set a “fire and safeguard risk index evaluation method.” The evaluation method has been applied in the world industry, which has attracted extensive research and discussion in various countries and promoted the development of the safety evaluation method. In 1974, based on the evaluation method of Dow Chemical Company, the Mond Department of British Imperial Chemical Company systematically put forward the “mond fire, explosion, and toxicity index evaluation method.” In 1976, the Ministry of Labour of Japan promulgated the “six-stage method for safety evaluation of chemical plants” and successively developed evaluation methods such as the pitian method. In the same year, the Netherlands proposed the danger evaluation method for chemical plants. In 1982, the European Community had promulgation the “directive on significant hazard sources in industrial activities.” In 1988 and 1990, the International Labour Organization separately promulgated the “guidelines for the control of major accidents” and the “practical protocol for preventing major industrial accidents.” All these ordinances put forward strict requirements for accident safety evaluation. Driven by systems safety engineering, the probabilistic risk assessment method has been developed for complex dynamic systems such as nuclear power plants and large chemical factories [23]. In parallel with the development of probabilistic risk assessment, fuzzy mathematics has been used in safety evaluation, greatly expanding the theoretical scope of safety evaluation. In addition, there is the safety index method proposed by Professor R.V. Romani, the man-machine-based safety evaluation proposed by Polish scholars, and the Japanese method of tunnel safety evaluation.In the early 1980s, safety systems engineering was introduced into China and was highly valued by many large and medium-sized enterprises and industry management departments. Based on the digestion and absorption of foreign safety inspection methods and safety analysis methods, relevant safety evaluation methods are applied to machinery, metallurgy, chemical industry, aerospace, and other industries. Many industries and local government departments have formulated safety checklists and evaluation standards. In 1986, the former Labor and personnel department separately issued scientific research projects such as the hazard level classification of machinery factories, the hazard level classification of chemical factories, and the hazard level classification of metallurgical factories to relevant scientific research units, to facilitate the extensive practice and application of safety evaluation methods in the safety management of Chinese enterprises. In 1987, the former Ministry of Machinery and Electronics first proposed to carry out the safety evaluation of machinery factories in the machinery industry. They promulgated the first ministerial safety evaluation standard, “safety evaluation standard of machinery factories,” in January 1, 1988. The promulgation and implementation of this standard marks that China’s machinery industry safety management has entered a new stage.With the development of society and the advancement of technology, safety evaluation has gradually penetrated various fields, especially the fields that require safe production. The field of coal mine safety production is no exception. Compared with other fields, the application of safety evaluation in the field of coal mine safety production is relatively backward. However, as real safety problems become more prominent, coal mine safety production has been paid more and more attention. In 1974, the British Chemical Industry Association first applied the theory of coal mine safety evaluation to coal mining enterprises and divided the coal mine safety evaluation into four grades: excellent, good, acceptable, and poor, and then made a qualitative evaluation according to the production status of the mine. In 1977, the United States promulgated “the federal mine safety and health act.” The main part of the act is the “scope of use of the provisional statutory safety standards for underground coal mines,” including various detailed inspection standards for coal mines. At the same time, each state government has also formulated state laws to supplement the “the federal mine safety and health act” according to local conditions. A good legal environment has greatly reduced coal mine accidents and improved the safety of coal mine production. China has also taken many measures in coal mine safety evaluation. In 1982 and 1986, the former Ministry of Coal Industry formulated and issued the “quality standards for mine ventilation and methods of inspection and assessment” and “production mine quality standardization standards,” separately. Since 1997, coal mine safety evaluation has been carried out nationwide, emphasizing the safety pre-evaluation, acceptance evaluation, special evaluation, and current situation evaluation of coal mine construction projects. In 2003, the China Coal Safety Supervision Bureau issued the “guidelines for safety quo evaluation” and supervised and managed the safety evaluation carried out by local safety supervision bureaus within their regions.The coal mining industry is a typical “three high” industry with high labor intensity, high employment risk, and high accident rate [24]. As a result, coal mine safety has always been the top priority of China’s work safety [25]. China has promulgated many laws and regulations. Coal enterprises are also trying to eliminate potential dangers, control accidents and reduce losses by improving process technology and equipment level, improving material performance, increasing automation and control degree, and increasing safety investment. Although the deteriorating situation of coal mine safety production has been initially curbed, the trend of the high occurrence of coal mine accidents and frequent occurrence of major and serious accidents has not been effectively curbed fundamentally. Many deep-seated problems have not been effectively solved. There is still a long way to go to tackle the problem of coal mine safety production.Coal mine safety is a complex system of interacting spatial and temporal factors [26]. The dimensions involved in coal mine safety are extensive, as shown in Figure 1. Everything from the design, manufacture, maintenance, inspection, and operation of equipment, as well as underground management, enterprise management, and even operation environment, social environment, economic factors, and political environment, as well as human factors, are all relevant to the occurrence of accidents in coal mines [27].Figure 1
Circulation diagram of the relationship between safety factors in coal mines.With China’s attention to mine accidents and the improvement of coal mechanization, the incidence of coal mine accidents has decreased, but coal mine production disasters still occur [28]. At the same time, with the increase of coal mining depth and the significant increase in technical difficulty of coal mine disaster prediction, coal mine safety evaluation is facing new challenges.Compared to foreign countries, research on coal mine safety evaluation started late in China. Although coal mine safety evaluation has developed rapidly in recent years through the tireless efforts of scholars, our level of research is still below international standards and the number of fatalities and mortality rates in coal mine accidents are higher than those in developed Western countries [29]. China has enacted laws and regulations to regulate coal production operations. Scientific researchers are also committed to minimizing the incidence of coal mine accidents by constantly learning the advanced production concepts and control methods of western developed countries. Scholars at home and abroad have done a lot of research on coal mine safety evaluation and achieved some results. Sari et al. determined the mine risk level for the first time by conducting a safety evaluation study of conventional and mechanized coal mining panels in two underground coal mines [30]. Sari et al. conducted an evaluation study using a 1390-day accident in an underground coal mine as an example. They proposed a method to establish an uncertainty model that includes the randomness of coal mine loss accidents [31]. Joy has developed a simple and practical process for conducting a qualitative risk assessment of the Australian coal mining industry [32]. Cheng and Yang applied rough set theory to select the optimal index and classified the risk level of the mine ventilation system through a support vector machine risk assessment model [33]. Ataei et al. proposed a coal mine safety evaluation model based on fuzzy logic [34]. To identify safety hazards, Zhou and Wang constructed a coal mine safety early warning system according to the characteristics of coal mine safety production. They used BP neural network algorithm to evaluate coal mine safety early warning [35]. Meng and Feng established an evaluation system for coal mine production safety using hierarchical analysis and a fuzzy comprehensive evaluation method. They applied it practically in evaluating coal mine production safety [36]. He et al. obtained the risk factors of coal mine safety management through a questionnaire survey and expert interviews and excavated the key points affecting coal mine safety management. The Page Rank algorithm and structural equation model are used to comprehensively evaluate the risk factors of coal mine safety management. The model is verified with the help of software tools [37]. Shao used the objectively weighted entropy weight-TOPSIS model to evaluate the safety production status of the mine [38]. Jia et al. used the subjectively empowered AHP-TOPSIS model to evaluate the safety quo rating of the mine [39]. Wang et al. established a mine safety management model. They used a fuzzy analytic hierarchy process to evaluate and sort the influencing factors, to verify the effectiveness of the fuzzy analytic hierarchy process in coal mine safety evaluation [40].The research object of coal mine safety evaluation is the safety problem of the whole coal mine production system [41]. In coal mine safety evaluation, it is about what criteria are used to determine how good or bad each specific safety factor is in the coal mine production system. In terms of selecting coal mine safety evaluation methods, many evaluation methods have been proposed at home and abroad. Currently, the methods used for coal mine safety evaluation can be divided into two main categories: qualitative and quantitative. The main characteristics of the qualitative evaluation method are that it is easy to understand, and easy to grasp, and the evaluation process is simple and easy to implement. However, there are certain shortcomings and limitations. The main manifestation is that it can be influenced by human experience, subjective preferences, and other factors, and the accuracy of its evaluation results is relatively low. Common methods include accident tree analysis and event tree analysis. These methods can qualitatively and semiquantitatively analyze the cause of the accident, analyze the logical relationship between the cause of the accident and the potential risk factors of the accident [42], establish the coal mine safety evaluation index [43], evaluate the dangerous state of the coal mine [44], etc., and realize the computerization of the problem analysis [45]. Quantitative evaluation is based on previous experimental data and accident statistics to conduct analytical modeling and construct the evaluation index system. The evaluation result is a quantitative index, such as how likely an accident is to occur, how extensive the impact of an accident is, the risk factor, the degree of mine safety, etc. Commonly used quantitative evaluation methods include the fuzzy comprehensive evaluation method [46], grey relation degree evaluation method, grey clustering evaluation method [47], neural network [48], and TOPSIS method [49]. Regarding the determination methods of evaluation index weight, there are mainly quantitative methods such as fuzzy analytic hierarchy process [50], entropy weight method [51], grey relation degree method [52], principal component analysis method [52], combined empowerment method [53], and euclidean distance method [54]. In addition, other methods commonly used for coal mine safety evaluation in recent years include extreme learning machines [55], BP neural networks [56], support vector machines [57], and so on. These methods are advantageous in coal mine safety evaluation due to the characteristics of short modeling time and high accuracy in predicting sample data.In coal mine safety evaluation work, whether the weight of the evaluation index is scientific and reasonable has a great impact on the evaluation results. At present, the commonly used evaluation methods have certain subjectivity and fuzziness. The calculation process is complex and not sufficiently accurate. The complexity of coal mine production systems, the diversity of safety influencing factors, and the nonlinearity of catastrophes make traditional safety evaluation methods less accurate, and the ability of a single evaluation method to solve practical problems still needs to be improved. BP neural network is a network widely connected by many neurons, which has the characteristics of strong associative memory and self-learning ability. For the given input and output samples, the neural network model solves the nonlinear problem well by automatically adjusting the weights to realize the mapping relationship between input and output. The technique for order preference by similarity to an ideal solution can rank the relative merits of existing multiple indexes. But its one-dimensional qualitative approach makes it more difficult to determine indicator weights in a multi-factor analysis. Based on the principle of game theory combination weight assignment, it is a game set of weights obtained by using a variety of different assignment methods to reconcile the inconsistencies between other assignment methods and finally achieve a satisfactory equilibrium result, which can solve the problem of weight determination in a more scientific, comprehensive and objective manner. The uncertainty of small sample data, many indexes, and ambiguous information can also be well addressed.Therefore, this paper introduces the method of determining weights by combining game theory. The three weight vectors obtained by the fuzzy analytic hierarchy process of subjective weight, the entropy weight method of objective weight and the BP neural network method of smart empowerment are aggregated through the game to obtain the optimal weight. At the same time, the “virtual negative ideal point” is defined to replace the traditional negative ideal point for improvement, to avoid the problem that the sample points are equidistant from the ideal point and negative ideal point and cannot be sorted when calculating the Euclidean distance. By applying the game theory combination weight and improved TOPSIS model to the analysis of coal mine safety evaluation examples, more objective and reasonable evaluation results can be obtained.


## 3. Methods

### 3.1. Fuzzy Analytic Hierarchy Process (FAHP)

The analytic hierarchy process (AHP) is a technique used for decision-making [58]. The method is widely used to determine weights for complex systems with multiple indexes. Under certain criteria, experts determine the relative importance of each index based on empirical subjective judgment to form a judgment matrix. The weight of each index is obtained under the premise of satisfying the consistency. The disadvantage is that the subjective randomness is strong, and the consistency of the judgment matrix is difficult to achieve, which is different from the consistency of human decision-making thinking. In contrast, the fuzzy analytic hierarchy process (FAHP) combines a fuzzy consistency matrix with the analytic hierarchy process. It not only retains the advantages of AHP, but also overcomes the ambiguity of traditional AHP in the judgment matrix, ensures the consistency of the judgment matrix, and is more in line with human decision-making thinking. The calculation process is as follows [50].


#### 3.1.1. Establishment of Fuzzy Complementary Matrix of Coal Mine Safety Evaluation Index

The safety evaluation indexesRi and Rj of n coal mines are compared in pairs, and aij are obtained by a quantitative description of the affiliation degree of fuzzy relationship using a 0.1∼0.9 scale. The fuzzy judgment matrix A=aijn×n of the coal mine safety evaluation index is constructed, in which 0≤aij≤1 and aij+aji=1 are satisfied.


#### 3.1.2. Fuzzy Consistent Judgment Matrix

The fuzzy complementary matrixA=aijn×n is summed by rows, the formula is ei=∑f=1naif,i,f=1,2,…,n, and then transformed according to formula (1) to obtain the fuzzy consistent judgment matrix E=eijn×n.(1)eij=ei−aij2n+0.5.Here,eij is the value of the index aij after the consistent processing; ei is the value of the fuzzy complementary matrix A=aijn×n summed by row.


#### 3.1.3. Calculation of the Weight of Each Index

The subjective weightβ=β1,β2,…,βn of FAHP is obtained by calculating the matrix E=eijn×n according to the following formula :(2)βi=2∑j=1neij−1nn−1i=1,2,…,n.Here,βi is the weight value corresponding to the ith index; eij is the value of the ith row and jth column of the matrix E.


### 3.2. Entropy Weight Method (EWM)

The entropy weight method (EWM) is an objective weighting method to determine the weight according to the principle of information entropy. It determines the weights based on the relationship between the original data and does not rely on human subjective judgment. The decision-making or evaluation results have a strong mathematical theoretical basis. The data used by the entropy weight method is the decision matrix, and the determined attribute weight reflects the degree of dispersion of attribute values. Based on the original data, information entropy is used to measure the amount of information. The specific definitions are as follows [59].Calculate the information entropyEj from the resulting normalized decision matrix R.(3)Ej=−k∑i=1mxijeijlnxijeij,eij=∑i=1mxij.Here,i=1,2,…,m;j=1,2,…,n;k>0,k=1/lnn, is a constant coefficient.Therefore, the weight coefficient value of the entropy weight method standardized for thejth evaluation index is(4)θj=1−Ej∑j=1n1−Ej.


### 3.3. Improved Composite Weight Method

Because of the different degrees of dispersion of the evaluation index values involved, using a fixed weight preference coefficient cannot fully reflect the information characteristics of the entropy weight method. To better combine the weights calculated by FAHP and EWM, the distance indexρj is used as the improved composite weight [51].According to the obtained weight coefficientβi of FAHP and weight coefficient θj of EWM, the composite weight ρj can be expressed as follows:(5)ρj=ξjβi2+1−ξjθj2.The dynamic weight preference coefficientξj is(6)ξj=θj2βi2+θj2.


### 3.4. Back Propagation Neural Network Method (BP-NN)

Back propagation neural network (BP-NN) can obtain the weight and structure of the network through learning and training. During the training process, the network continuously adjusts the connection strength and threshold between the input layer node and the hidden layer node, the hidden layer node, and the output layer node through repeated learning. When the input standardization scheme index value has been trained, and the required network accuracy has been achieved, the final connection weight matrixV between the input layer and the hidden layer is obtained based on the adjustment. By calculating the sum of the absolute values of the connection weights between each input layer node and all hidden layer nodes, and normalizing them, the weights of m indexes are obtained [60]. The calculation formula is as follows:(7)δi=∑l=1kvjl∑i=1m∑l=1kvil,j=1,2,…,m.Here,v represents the connection weight between each input layer node and all hidden layer nodes. k represents the number of nodes contained in the hidden layer.


### 3.5. Combination Weight Method Based on Game Theory

The combination weight method based on game theory is to unify and coordinate the weights of various indexes obtained by multiple weighting methods, and to find the maximum common interests point among the indexes. This method can scientifically optimize the combination of subjective and objective weights, to improve the rationality of the index weighted. The combination weighting steps are as follows [56].


#### 3.5.1. Calculate Index Weight

The weights of the safety evaluation indexes for each mine were calculated using three methods: FAHP, EWM, and BP-NN method. Basic weight vector setwk=wk1,wk2,…,wknk=1,2,…,L, n is the number of coal mine safety evaluation indexes, and L is the number of methods to calculate the weight. Set the linear combination weight coefficient α=α1,α2,…,αL. Any linear combination of these vectors is as follows:(8)w=∑k=1nαkwkT.Here,w is the linear combination of weights. αk is the weight coefficient.


#### 3.5.2. Optimized Combination

The optimal combination of different weights is carried out. Aiming at minimizing the deviation betweenw and wk, the L linear weight combination coefficients in equation (6) are optimized to obtain the most satisfactory weight in w. The objective function formula obtained is as follows:(9)min∑k=1nαkwkT−wk2,k=1,2,…,L.


#### 3.5.3. Normalization Processing

According to formula (10), the calculated optimized combination coefficients are normalized.(10)αk∗=αk∑k=1nαk.Finally, the weights of the game theory combination weighting are obtained by the following formula :(11)w∗=∑k=1nαk∗wkT.


### 3.6. Technique for Order Preference by Similarity to an Ideal Solution Method (TOPSIS)

The principle of the technique for order preference by similarity to an ideal solution method (TOPSIS) is to rank evaluation objects using their relative distance from the positive and negative ideal solution of the scheme. Each index of the positive ideal solution is usually taken to be the best value of the evaluation scheme. The negative ideal solution is the worst value of each index in the scheme to be evaluated. The TOPSIS method judges the quality of the scheme by detecting the relative closeness of the scheme to be evaluated to the positive and negative ideal solutions. Obviously, the closer the solution is to the positive ideal solution, the better the solution is [61].Assuming that there arem evaluation objects, the set of objects M=M1,M2,…,Mm. There are n evaluation indexes, then the set of indexes R=R1,R2,…,Rn. Mm corresponds to Rn decision value bmn, then the constructed decision matrix B=bijm×n.The initial matrixB is further transformed according to formula (12) to construct a standardized decision matrix C=xijm×n.(12)xij=bmn−bnminbnmax−bnmin,benefit index,bnmax−bmnbnmax−bnmin,cost index.Here,xij is the value of the jth column of the ith row of the matrix C. bmn is the nth index value of the mth evaluation object. bnmin represents the minimum value of n indexes in the sample. bnmax represents the maximum value of n indexes in the sample.Multiply the matrixC by the weights to get the weighted normalized decision matrix Y=yijm×n.(13)yij=wjxiji=1,2,…,m;j=1,2,…,n.Here,yij is the value of the jth column of the ith row of the matrix Y. wj is the combination weight corresponding to the index in the jth column. xij is the value of the jth column of the ith row of the matrix C.According to formula (14), the “positive ideal solution” and “negative ideal solution” of each index are calculated.(14)R+=maxirij′|i∈1,m;j∈1,n,R−=minirij′|i∈1,m;j∈1,n.Here,R+ represents a positive ideal solution. R− represents the negative ideal solution.Then, the distance between each evaluation object and the positive and negative ideal solution can be expressed by the following equation:(15)di+=∑j=1nεjrij′−rj+2,di−=∑j=1nεjrij′−rj−2.Here,di+ and di−, respectively, represent the distance between the ith evaluation object and the positive and negative ideal solutions. rj+ and rj− are the index values corresponding to R+ and R−, respectively. The calculation formula of relative paste progress ci is as follows:(16)ci=di−di++di−,i∈1,m.The value range of the relative paste progressci of the object to be evaluated is (0, 1). The closer to 1 means that the object is closer to the positive ideal solution, the better the object to be evaluated and the better the safety level.


## 3.1. Fuzzy Analytic Hierarchy Process (FAHP)

The analytic hierarchy process (AHP) is a technique used for decision-making [58]. The method is widely used to determine weights for complex systems with multiple indexes. Under certain criteria, experts determine the relative importance of each index based on empirical subjective judgment to form a judgment matrix. The weight of each index is obtained under the premise of satisfying the consistency. The disadvantage is that the subjective randomness is strong, and the consistency of the judgment matrix is difficult to achieve, which is different from the consistency of human decision-making thinking. In contrast, the fuzzy analytic hierarchy process (FAHP) combines a fuzzy consistency matrix with the analytic hierarchy process. It not only retains the advantages of AHP, but also overcomes the ambiguity of traditional AHP in the judgment matrix, ensures the consistency of the judgment matrix, and is more in line with human decision-making thinking. The calculation process is as follows [50].


### 3.1.1. Establishment of Fuzzy Complementary Matrix of Coal Mine Safety Evaluation Index

The safety evaluation indexesRi and Rj of n coal mines are compared in pairs, and aij are obtained by a quantitative description of the affiliation degree of fuzzy relationship using a 0.1∼0.9 scale. The fuzzy judgment matrix A=aijn×n of the coal mine safety evaluation index is constructed, in which 0≤aij≤1 and aij+aji=1 are satisfied.


### 3.1.2. Fuzzy Consistent Judgment Matrix

The fuzzy complementary matrixA=aijn×n is summed by rows, the formula is ei=∑f=1naif,i,f=1,2,…,n, and then transformed according to formula (1) to obtain the fuzzy consistent judgment matrix E=eijn×n.(1)eij=ei−aij2n+0.5.Here,eij is the value of the index aij after the consistent processing; ei is the value of the fuzzy complementary matrix A=aijn×n summed by row.


### 3.1.3. Calculation of the Weight of Each Index

The subjective weightβ=β1,β2,…,βn of FAHP is obtained by calculating the matrix E=eijn×n according to the following formula :(2)βi=2∑j=1neij−1nn−1i=1,2,…,n.Here,βi is the weight value corresponding to the ith index; eij is the value of the ith row and jth column of the matrix E.


## 3.1.1. Establishment of Fuzzy Complementary Matrix of Coal Mine Safety Evaluation Index

The safety evaluation indexesRi and Rj of n coal mines are compared in pairs, and aij are obtained by a quantitative description of the affiliation degree of fuzzy relationship using a 0.1∼0.9 scale. The fuzzy judgment matrix A=aijn×n of the coal mine safety evaluation index is constructed, in which 0≤aij≤1 and aij+aji=1 are satisfied.


## 3.1.2. Fuzzy Consistent Judgment Matrix

The fuzzy complementary matrixA=aijn×n is summed by rows, the formula is ei=∑f=1naif,i,f=1,2,…,n, and then transformed according to formula (1) to obtain the fuzzy consistent judgment matrix E=eijn×n.(1)eij=ei−aij2n+0.5.Here,eij is the value of the index aij after the consistent processing; ei is the value of the fuzzy complementary matrix A=aijn×n summed by row.


## 3.1.3. Calculation of the Weight of Each Index

The subjective weightβ=β1,β2,…,βn of FAHP is obtained by calculating the matrix E=eijn×n according to the following formula :(2)βi=2∑j=1neij−1nn−1i=1,2,…,n.Here,βi is the weight value corresponding to the ith index; eij is the value of the ith row and jth column of the matrix E.


## 3.2. Entropy Weight Method (EWM)

The entropy weight method (EWM) is an objective weighting method to determine the weight according to the principle of information entropy. It determines the weights based on the relationship between the original data and does not rely on human subjective judgment. The decision-making or evaluation results have a strong mathematical theoretical basis. The data used by the entropy weight method is the decision matrix, and the determined attribute weight reflects the degree of dispersion of attribute values. Based on the original data, information entropy is used to measure the amount of information. The specific definitions are as follows [59].Calculate the information entropyEj from the resulting normalized decision matrix R.(3)Ej=−k∑i=1mxijeijlnxijeij,eij=∑i=1mxij.Here,i=1,2,…,m;j=1,2,…,n;k>0,k=1/lnn, is a constant coefficient.Therefore, the weight coefficient value of the entropy weight method standardized for thejth evaluation index is(4)θj=1−Ej∑j=1n1−Ej.


## 3.3. Improved Composite Weight Method

Because of the different degrees of dispersion of the evaluation index values involved, using a fixed weight preference coefficient cannot fully reflect the information characteristics of the entropy weight method. To better combine the weights calculated by FAHP and EWM, the distance indexρj is used as the improved composite weight [51].According to the obtained weight coefficientβi of FAHP and weight coefficient θj of EWM, the composite weight ρj can be expressed as follows:(5)ρj=ξjβi2+1−ξjθj2.The dynamic weight preference coefficientξj is(6)ξj=θj2βi2+θj2.


## 3.4. Back Propagation Neural Network Method (BP-NN)

Back propagation neural network (BP-NN) can obtain the weight and structure of the network through learning and training. During the training process, the network continuously adjusts the connection strength and threshold between the input layer node and the hidden layer node, the hidden layer node, and the output layer node through repeated learning. When the input standardization scheme index value has been trained, and the required network accuracy has been achieved, the final connection weight matrixV between the input layer and the hidden layer is obtained based on the adjustment. By calculating the sum of the absolute values of the connection weights between each input layer node and all hidden layer nodes, and normalizing them, the weights of m indexes are obtained [60]. The calculation formula is as follows:(7)δi=∑l=1kvjl∑i=1m∑l=1kvil,j=1,2,…,m.Here,v represents the connection weight between each input layer node and all hidden layer nodes. k represents the number of nodes contained in the hidden layer.


## 3.5. Combination Weight Method Based on Game Theory

The combination weight method based on game theory is to unify and coordinate the weights of various indexes obtained by multiple weighting methods, and to find the maximum common interests point among the indexes. This method can scientifically optimize the combination of subjective and objective weights, to improve the rationality of the index weighted. The combination weighting steps are as follows [56].


### 3.5.1. Calculate Index Weight

The weights of the safety evaluation indexes for each mine were calculated using three methods: FAHP, EWM, and BP-NN method. Basic weight vector setwk=wk1,wk2,…,wknk=1,2,…,L, n is the number of coal mine safety evaluation indexes, and L is the number of methods to calculate the weight. Set the linear combination weight coefficient α=α1,α2,…,αL. Any linear combination of these vectors is as follows:(8)w=∑k=1nαkwkT.Here,w is the linear combination of weights. αk is the weight coefficient.


### 3.5.2. Optimized Combination

The optimal combination of different weights is carried out. Aiming at minimizing the deviation betweenw and wk, the L linear weight combination coefficients in equation (6) are optimized to obtain the most satisfactory weight in w. The objective function formula obtained is as follows:(9)min∑k=1nαkwkT−wk2,k=1,2,…,L.


### 3.5.3. Normalization Processing

According to formula (10), the calculated optimized combination coefficients are normalized.(10)αk∗=αk∑k=1nαk.Finally, the weights of the game theory combination weighting are obtained by the following formula :(11)w∗=∑k=1nαk∗wkT.


## 3.5.1. Calculate Index Weight

The weights of the safety evaluation indexes for each mine were calculated using three methods: FAHP, EWM, and BP-NN method. Basic weight vector setwk=wk1,wk2,…,wknk=1,2,…,L, n is the number of coal mine safety evaluation indexes, and L is the number of methods to calculate the weight. Set the linear combination weight coefficient α=α1,α2,…,αL. Any linear combination of these vectors is as follows:(8)w=∑k=1nαkwkT.Here,w is the linear combination of weights. αk is the weight coefficient.


## 3.5.2. Optimized Combination

The optimal combination of different weights is carried out. Aiming at minimizing the deviation betweenw and wk, the L linear weight combination coefficients in equation (6) are optimized to obtain the most satisfactory weight in w. The objective function formula obtained is as follows:(9)min∑k=1nαkwkT−wk2,k=1,2,…,L.


## 3.5.3. Normalization Processing

According to formula (10), the calculated optimized combination coefficients are normalized.(10)αk∗=αk∑k=1nαk.Finally, the weights of the game theory combination weighting are obtained by the following formula :(11)w∗=∑k=1nαk∗wkT.


## 3.6. Technique for Order Preference by Similarity to an Ideal Solution Method (TOPSIS)

The principle of the technique for order preference by similarity to an ideal solution method (TOPSIS) is to rank evaluation objects using their relative distance from the positive and negative ideal solution of the scheme. Each index of the positive ideal solution is usually taken to be the best value of the evaluation scheme. The negative ideal solution is the worst value of each index in the scheme to be evaluated. The TOPSIS method judges the quality of the scheme by detecting the relative closeness of the scheme to be evaluated to the positive and negative ideal solutions. Obviously, the closer the solution is to the positive ideal solution, the better the solution is [61].Assuming that there arem evaluation objects, the set of objects M=M1,M2,…,Mm. There are n evaluation indexes, then the set of indexes R=R1,R2,…,Rn. Mm corresponds to Rn decision value bmn, then the constructed decision matrix B=bijm×n.The initial matrixB is further transformed according to formula (12) to construct a standardized decision matrix C=xijm×n.(12)xij=bmn−bnminbnmax−bnmin,benefit index,bnmax−bmnbnmax−bnmin,cost index.Here,xij is the value of the jth column of the ith row of the matrix C. bmn is the nth index value of the mth evaluation object. bnmin represents the minimum value of n indexes in the sample. bnmax represents the maximum value of n indexes in the sample.Multiply the matrixC by the weights to get the weighted normalized decision matrix Y=yijm×n.(13)yij=wjxiji=1,2,…,m;j=1,2,…,n.Here,yij is the value of the jth column of the ith row of the matrix Y. wj is the combination weight corresponding to the index in the jth column. xij is the value of the jth column of the ith row of the matrix C.According to formula (14), the “positive ideal solution” and “negative ideal solution” of each index are calculated.(14)R+=maxirij′|i∈1,m;j∈1,n,R−=minirij′|i∈1,m;j∈1,n.Here,R+ represents a positive ideal solution. R− represents the negative ideal solution.Then, the distance between each evaluation object and the positive and negative ideal solution can be expressed by the following equation:(15)di+=∑j=1nεjrij′−rj+2,di−=∑j=1nεjrij′−rj−2.Here,di+ and di−, respectively, represent the distance between the ith evaluation object and the positive and negative ideal solutions. rj+ and rj− are the index values corresponding to R+ and R−, respectively. The calculation formula of relative paste progress ci is as follows:(16)ci=di−di++di−,i∈1,m.The value range of the relative paste progressci of the object to be evaluated is (0, 1). The closer to 1 means that the object is closer to the positive ideal solution, the better the object to be evaluated and the better the safety level.


## 4. Example Verification

### 4.1. Technique for Order Preference by Similarity to an Ideal Solution Method (TOPSIS)

The calculation flow chart of the example in this paper is shown in Figure2. The data collected from 5 mines under Zheng Coal Group were used as application samples to verify the practicability and rationality of the TOPSIS model based on game theory combination weighting for a comprehensive evaluation of coal mine safety. Firstly, under the guidance of safety system theory, 20 comprehensive evaluation indexes of coal mine safety were selected for verification and analysis from four aspects: human, machine, environment, and management. Secondly, the levels of coal mine safety are divided into five grades according to the characteristics of coal mine safety production, namely, grade I (safe), grade II (relatively safe), grade III (moderately safe), grade IV (generally safe), and grade V (unsafe). The critical value of the safety level of each evaluation index shall be determined concerning the relevant regulations [62]. The initial raw data of 20 evaluation indexes of 5 coal mines and the classification standards of each index are shown in Table 1.Figure 2
Example calculation flow chart.Table 1
Original data of each index and critical value of safety grade classification standard.
Primary indexSecondary indexIndex typeMine 1Mine 2Mine 3Mine 4Mine 5Grade IGrade IIGrade IIIGrade IVGrade VHuman factorThe rate of “three violations” by personnelW1 (%)09.24.95.82.55.6<44∼88∼1212∼16>16The average monthly training time of employeesW2 (h)14.68.76.88.57.7>97∼95∼73∼5<3The average length of serviceW3 (a)15.04.94.65.94.6>106∼104∼62∼4<2Equipment factorIntact rate of lifting equipmentW4 (%)18483859289>9590∼9585∼9080∼85<80Intact rate of transportation equipmentW5 (%)18189909190>9590∼9585∼9080∼85<80Intact rate of electromechanical equipmentW6 (%)18089819088>9590∼9585∼9080∼85<80Intact rate of ventilation equipmentW7 (%)18084818882>9590∼9585∼9080∼85<80Intact rate of drainage equipmentW8 (%)18187828085>9590∼9585∼9080∼85<80Intact rate of fire prevention and fire fighting equipmentW9 (%)17885798182>9590∼9585∼9080∼85<80Environmental factorThe dip angle of coal seamW10 (degree)02823261121<88∼2525∼4545∼75>75Normal water inflow of mineW11 (m3/h)11793463705301537<2020∼180180∼600600∼1200>1200The shortest spontaneous combustion period of coal seamW12 (month)0486108>97∼95∼73∼5<3Maximum dust concentration of working faceW13 (mg/m3)11081059<44∼66∼88∼10>10Reliability rate of top plateW14 (%)18084868285>9590∼9585∼9080∼85<80Ten thousand tons of gas outburst concentrationW15 (%)02.04.52.58.12.9<0.50.5∼11∼22∼3>3Management factorPerfection rate of safety systemW16 (%)16579668877>9080∼9070∼8060∼70<60Perfection rate of safety measuresW17 (%)16885737973>9080∼9070∼8060∼70<60Efficient safety managementW18 (%)17077718375>9080∼9070∼8060∼70<60Timeliness of safety managementW19 (%)16878768980>9080∼9070∼8060∼70<60Perfection rate of emergency mechanismW20 (%)17984739286>9080∼9070∼8060∼70<60Note. “0” is the benefit index. “1” is a cost indicator. Data sources: Zheng Coal Group internal information, obtained by collation, for 2018.


### 4.2. Calculation of the Weight of the Evaluation Index

Firstly, the subjective weightsβi of the 20 evaluation indexes are obtained by using FAHP. Secondly, the EWM is used to obtain the objective weight θj of each index according to the sample data of each mine index. To overcome the shortcomings of EWM in evaluating scattered index data, the weights calculated by FAHP and EWM are combined using formula (5) and formula (6) to obtain the improved composite weight ρj. Then, taking the evaluation results obtained by FAHP as the target value, the sample data are trained by MATLAB to get the weight δi. Finally, the subjective weight βi, objective weight θj , and smart empowerment weights δi of the indexes are calculated based on the theory of game theory according to formulas (8)–(11) to obtain the combination weight w∗. The calculation process was implemented using Matlab programming, and the results of the index weights of the various methods are shown in Table 2.Table 2
Calculation results of index weights.
IndexSubjective weightβiObjective weightθjSmart empowerment weightδiImprove composite weightρjCombination weightw∗W10.09340.04950.03940.03250.0473W20.05610.04110.03920.02670.0423W30.03890.04080.04300.01490.0431W40.01630.03120.04800.01210.0487W50.00420.05580.05070.00030.0370W60.01050.03980.03490.00350.0266W70.02190.05350.04360.00570.0335W80.01400.03920.04560.00710.0412W90.02050.06280.04740.00400.0333W100.00320.03960.05890.00050.0551W110.01920.07200.05320.00260.0357W120.00570.03310.06140.00130.0621W130.00210.04310.04940.00010.0412W140.00710.03870.05580.00220.0526W150.05930.06680.05450.01720.0495W160.01400.03800.05730.00470.0565W170.03930.03970.03570.02000.0346W180.08200.04020.05790.03180.0725W190.07130.03920.06790.03900.0830W200.02600.05070.05600.00130.0514


### 4.3. Safety Evaluation Results of Coal Mine

#### 4.3.1. Coal Mine Safety Evaluation Based on FAHP

The original data for the 20 indexes from the five mine samples were used to derive the standardized decision matrixC1 according to formula (12). Then, C1 is multiplied by the weight βi calculated by FAHP to obtain the comprehensive evaluation score of each mine, as shown in Table 3.Table 3
Safety comprehensive evaluation scores of different methods in each mine.
MethodNameMine 1Mine 2Mine 3Mine 4Mine 5FAHP method0.12030.11780.10770.14120.1179Improved composite weight-TOPSIS method0.56000.70970.70110.78020.7058Game theory combination weight-TOPSIS method0.58400.75280.66400.80060.7033


#### 4.3.2. Coal Mine Safety Evaluation Based on TOPSIS Method

The improved composite weight method and the index weights determined based on the game theory combined weighting method are combined with the TOPSIS method to establish the improved composite weight-TOPSIS evaluation model and the game theory combination weight-TOPSIS evaluation model, respectively. The 20 evaluation indexes of the five mines were combined with the critical values of the safety grading criteria of each index to form an augmented matrix. After forming the initial decision matrixB of the coal mine safety grade, the standardized decision matrix C2 is then dimensionless formed according to formula (12).(1)
Coal mine safety evaluation based on improved composite weight-TOPSIS method. The weighted standardized decision matrixY1 is derived using formula (13) based on the improved composite weights ρj obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.(2)
Coal mine safety evaluation based on game theory combination weight-TOPSIS method. The weighted standardized decision matrixY2 is derived using formula (13) based on the game theory combination weights w∗ obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.


### 4.4. Result Analysis

#### 4.4.1. Analysis of Coal Mine Safety Evaluation Index

To make the results more intuitive, the weight of the coal mine safety evaluation index calculated by various methods in chapter 4.2 is visualized, as shown in Figure3.Figure 3
Weights of safety evaluation index under different methods in each mine.It can be seen from the weight curve trend of each index in Figure3 that the management factor has the greatest impact on the safety evaluation results of coal mines. According to accident causation theory [63], it can be explained that human unsafe behavior, unsafe state of equipment, and unsafe production environments will eventually lead to accidents due to the distortion of information transmission and management errors. Environmental factors and human factors also have a relatively large impact on the results of coal mine safety evaluations, which further reflects the harsh environment of coal mine production in China and the relatively weak safety awareness of coal miners. The equipment factor is less influential than other factors, but it should not be ignored. This is because a good production equipment system guarantees safe coal mine production.At the same time, secondary index factors such as efficiency of safety management, Timeliness of safety management, intact rate of the equipment, and the rate of “three violations” by personnel have a greater impact on the safety evaluation of a coal mine.


#### 4.4.2. Comparison of the Results of Three Coal Mine Safety Evaluation Methods

The comprehensive evaluation scores of coal mine safety in Table3 are visualized, as shown in Figure 4. The evaluation results of 5 coal mines obtained by the three methods are compared and analyzed.Figure 4
Comprehensive evaluation scores of coal mine safety based on three methods.It can be seen from Figure4 that the comprehensive evaluation score curves of the three methods are consistent with each other. Among them, the improved composite weight-TOPSIS method and the game theory combination weight-TOPSIS method have large fluctuations in the comprehensive evaluation score curve. That is, they can clearly distinguish the pros and cons of the evaluation objects. The evaluation score curve of the FAHP method tends to be relatively stable, which is not conducive to distinguishing the strengths and weaknesses of the evaluated objects. Compared with the improved composite weight-TOPSIS method, the discrimination of comprehensive evaluation scores is greater for the game theory combination weight-TOPSIS method of five sample mines. It has the characteristics of higher scores for mines with better evaluation and lower scores for mines with poor evaluation.


#### 4.4.3. Determination of Coal Mine Safety Evaluation Grade

After comparing the three methods, the results obtained by the game theory combination weight-TOPSIS method have the largest discreteness and obvious discrimination. Therefore, combined with the quantitative standards of each safety level, the safety evaluation levels of five mines are calculated, and the results are shown in Table4.Table 4
Safety evaluation grade results of each mine.
MineεiSafety evaluation gradeMine 10.5840Grade IVMine 20.7528Grade IIIMine 30.6640Grade IVMine 40.8006Grade IIMine 50.7033Grade IIIGrade I0.8735The critical value of safety gradeGrade II0.7904Grade III0.6643Grade IV0.5331It can be seen from Table4 that the safety grade of the five mine samples is ranked as follows: mine 4 > grade II (relatively safe) > mine 2 > mine 5 > grade III (moderately safe) > mine 3 > mine 1 > grade IV (generally safe). The safety grade of mine 4 is grade II and has maintained a good safety condition for a long time. The safety status of other coal mines needs to be improved. The evaluation results are consistent with the actual situation, indicating that the model is accurate for the comprehensive safety evaluation of coal mines and can be applied to guide coal mine safety production.


## 4.1. Technique for Order Preference by Similarity to an Ideal Solution Method (TOPSIS)

The calculation flow chart of the example in this paper is shown in Figure2. The data collected from 5 mines under Zheng Coal Group were used as application samples to verify the practicability and rationality of the TOPSIS model based on game theory combination weighting for a comprehensive evaluation of coal mine safety. Firstly, under the guidance of safety system theory, 20 comprehensive evaluation indexes of coal mine safety were selected for verification and analysis from four aspects: human, machine, environment, and management. Secondly, the levels of coal mine safety are divided into five grades according to the characteristics of coal mine safety production, namely, grade I (safe), grade II (relatively safe), grade III (moderately safe), grade IV (generally safe), and grade V (unsafe). The critical value of the safety level of each evaluation index shall be determined concerning the relevant regulations [62]. The initial raw data of 20 evaluation indexes of 5 coal mines and the classification standards of each index are shown in Table 1.Figure 2
Example calculation flow chart.Table 1
Original data of each index and critical value of safety grade classification standard.
Primary indexSecondary indexIndex typeMine 1Mine 2Mine 3Mine 4Mine 5Grade IGrade IIGrade IIIGrade IVGrade VHuman factorThe rate of “three violations” by personnelW1 (%)09.24.95.82.55.6<44∼88∼1212∼16>16The average monthly training time of employeesW2 (h)14.68.76.88.57.7>97∼95∼73∼5<3The average length of serviceW3 (a)15.04.94.65.94.6>106∼104∼62∼4<2Equipment factorIntact rate of lifting equipmentW4 (%)18483859289>9590∼9585∼9080∼85<80Intact rate of transportation equipmentW5 (%)18189909190>9590∼9585∼9080∼85<80Intact rate of electromechanical equipmentW6 (%)18089819088>9590∼9585∼9080∼85<80Intact rate of ventilation equipmentW7 (%)18084818882>9590∼9585∼9080∼85<80Intact rate of drainage equipmentW8 (%)18187828085>9590∼9585∼9080∼85<80Intact rate of fire prevention and fire fighting equipmentW9 (%)17885798182>9590∼9585∼9080∼85<80Environmental factorThe dip angle of coal seamW10 (degree)02823261121<88∼2525∼4545∼75>75Normal water inflow of mineW11 (m3/h)11793463705301537<2020∼180180∼600600∼1200>1200The shortest spontaneous combustion period of coal seamW12 (month)0486108>97∼95∼73∼5<3Maximum dust concentration of working faceW13 (mg/m3)11081059<44∼66∼88∼10>10Reliability rate of top plateW14 (%)18084868285>9590∼9585∼9080∼85<80Ten thousand tons of gas outburst concentrationW15 (%)02.04.52.58.12.9<0.50.5∼11∼22∼3>3Management factorPerfection rate of safety systemW16 (%)16579668877>9080∼9070∼8060∼70<60Perfection rate of safety measuresW17 (%)16885737973>9080∼9070∼8060∼70<60Efficient safety managementW18 (%)17077718375>9080∼9070∼8060∼70<60Timeliness of safety managementW19 (%)16878768980>9080∼9070∼8060∼70<60Perfection rate of emergency mechanismW20 (%)17984739286>9080∼9070∼8060∼70<60Note. “0” is the benefit index. “1” is a cost indicator. Data sources: Zheng Coal Group internal information, obtained by collation, for 2018.


## 4.2. Calculation of the Weight of the Evaluation Index

Firstly, the subjective weightsβi of the 20 evaluation indexes are obtained by using FAHP. Secondly, the EWM is used to obtain the objective weight θj of each index according to the sample data of each mine index. To overcome the shortcomings of EWM in evaluating scattered index data, the weights calculated by FAHP and EWM are combined using formula (5) and formula (6) to obtain the improved composite weight ρj. Then, taking the evaluation results obtained by FAHP as the target value, the sample data are trained by MATLAB to get the weight δi. Finally, the subjective weight βi, objective weight θj , and smart empowerment weights δi of the indexes are calculated based on the theory of game theory according to formulas (8)–(11) to obtain the combination weight w∗. The calculation process was implemented using Matlab programming, and the results of the index weights of the various methods are shown in Table 2.Table 2
Calculation results of index weights.
IndexSubjective weightβiObjective weightθjSmart empowerment weightδiImprove composite weightρjCombination weightw∗W10.09340.04950.03940.03250.0473W20.05610.04110.03920.02670.0423W30.03890.04080.04300.01490.0431W40.01630.03120.04800.01210.0487W50.00420.05580.05070.00030.0370W60.01050.03980.03490.00350.0266W70.02190.05350.04360.00570.0335W80.01400.03920.04560.00710.0412W90.02050.06280.04740.00400.0333W100.00320.03960.05890.00050.0551W110.01920.07200.05320.00260.0357W120.00570.03310.06140.00130.0621W130.00210.04310.04940.00010.0412W140.00710.03870.05580.00220.0526W150.05930.06680.05450.01720.0495W160.01400.03800.05730.00470.0565W170.03930.03970.03570.02000.0346W180.08200.04020.05790.03180.0725W190.07130.03920.06790.03900.0830W200.02600.05070.05600.00130.0514


## 4.3. Safety Evaluation Results of Coal Mine

### 4.3.1. Coal Mine Safety Evaluation Based on FAHP

The original data for the 20 indexes from the five mine samples were used to derive the standardized decision matrixC1 according to formula (12). Then, C1 is multiplied by the weight βi calculated by FAHP to obtain the comprehensive evaluation score of each mine, as shown in Table 3.Table 3
Safety comprehensive evaluation scores of different methods in each mine.
MethodNameMine 1Mine 2Mine 3Mine 4Mine 5FAHP method0.12030.11780.10770.14120.1179Improved composite weight-TOPSIS method0.56000.70970.70110.78020.7058Game theory combination weight-TOPSIS method0.58400.75280.66400.80060.7033


### 4.3.2. Coal Mine Safety Evaluation Based on TOPSIS Method

The improved composite weight method and the index weights determined based on the game theory combined weighting method are combined with the TOPSIS method to establish the improved composite weight-TOPSIS evaluation model and the game theory combination weight-TOPSIS evaluation model, respectively. The 20 evaluation indexes of the five mines were combined with the critical values of the safety grading criteria of each index to form an augmented matrix. After forming the initial decision matrixB of the coal mine safety grade, the standardized decision matrix C2 is then dimensionless formed according to formula (12).(1)
Coal mine safety evaluation based on improved composite weight-TOPSIS method. The weighted standardized decision matrixY1 is derived using formula (13) based on the improved composite weights ρj obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.(2)
Coal mine safety evaluation based on game theory combination weight-TOPSIS method. The weighted standardized decision matrixY2 is derived using formula (13) based on the game theory combination weights w∗ obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.


## 4.3.1. Coal Mine Safety Evaluation Based on FAHP

The original data for the 20 indexes from the five mine samples were used to derive the standardized decision matrixC1 according to formula (12). Then, C1 is multiplied by the weight βi calculated by FAHP to obtain the comprehensive evaluation score of each mine, as shown in Table 3.Table 3
Safety comprehensive evaluation scores of different methods in each mine.
MethodNameMine 1Mine 2Mine 3Mine 4Mine 5FAHP method0.12030.11780.10770.14120.1179Improved composite weight-TOPSIS method0.56000.70970.70110.78020.7058Game theory combination weight-TOPSIS method0.58400.75280.66400.80060.7033


## 4.3.2. Coal Mine Safety Evaluation Based on TOPSIS Method

The improved composite weight method and the index weights determined based on the game theory combined weighting method are combined with the TOPSIS method to establish the improved composite weight-TOPSIS evaluation model and the game theory combination weight-TOPSIS evaluation model, respectively. The 20 evaluation indexes of the five mines were combined with the critical values of the safety grading criteria of each index to form an augmented matrix. After forming the initial decision matrixB of the coal mine safety grade, the standardized decision matrix C2 is then dimensionless formed according to formula (12).(1)
Coal mine safety evaluation based on improved composite weight-TOPSIS method. The weighted standardized decision matrixY1 is derived using formula (13) based on the improved composite weights ρj obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.(2)
Coal mine safety evaluation based on game theory combination weight-TOPSIS method. The weighted standardized decision matrixY2 is derived using formula (13) based on the game theory combination weights w∗ obtained in chapter 4.2. The comprehensive evaluation score of each mine is then calculated by combining formulas (14)–(16), as shown in Table 3.


## 4.4. Result Analysis

### 4.4.1. Analysis of Coal Mine Safety Evaluation Index

To make the results more intuitive, the weight of the coal mine safety evaluation index calculated by various methods in chapter 4.2 is visualized, as shown in Figure3.Figure 3
Weights of safety evaluation index under different methods in each mine.It can be seen from the weight curve trend of each index in Figure3 that the management factor has the greatest impact on the safety evaluation results of coal mines. According to accident causation theory [63], it can be explained that human unsafe behavior, unsafe state of equipment, and unsafe production environments will eventually lead to accidents due to the distortion of information transmission and management errors. Environmental factors and human factors also have a relatively large impact on the results of coal mine safety evaluations, which further reflects the harsh environment of coal mine production in China and the relatively weak safety awareness of coal miners. The equipment factor is less influential than other factors, but it should not be ignored. This is because a good production equipment system guarantees safe coal mine production.At the same time, secondary index factors such as efficiency of safety management, Timeliness of safety management, intact rate of the equipment, and the rate of “three violations” by personnel have a greater impact on the safety evaluation of a coal mine.


### 4.4.2. Comparison of the Results of Three Coal Mine Safety Evaluation Methods

The comprehensive evaluation scores of coal mine safety in Table3 are visualized, as shown in Figure 4. The evaluation results of 5 coal mines obtained by the three methods are compared and analyzed.Figure 4
Comprehensive evaluation scores of coal mine safety based on three methods.It can be seen from Figure4 that the comprehensive evaluation score curves of the three methods are consistent with each other. Among them, the improved composite weight-TOPSIS method and the game theory combination weight-TOPSIS method have large fluctuations in the comprehensive evaluation score curve. That is, they can clearly distinguish the pros and cons of the evaluation objects. The evaluation score curve of the FAHP method tends to be relatively stable, which is not conducive to distinguishing the strengths and weaknesses of the evaluated objects. Compared with the improved composite weight-TOPSIS method, the discrimination of comprehensive evaluation scores is greater for the game theory combination weight-TOPSIS method of five sample mines. It has the characteristics of higher scores for mines with better evaluation and lower scores for mines with poor evaluation.


### 4.4.3. Determination of Coal Mine Safety Evaluation Grade

After comparing the three methods, the results obtained by the game theory combination weight-TOPSIS method have the largest discreteness and obvious discrimination. Therefore, combined with the quantitative standards of each safety level, the safety evaluation levels of five mines are calculated, and the results are shown in Table4.Table 4
Safety evaluation grade results of each mine.
MineεiSafety evaluation gradeMine 10.5840Grade IVMine 20.7528Grade IIIMine 30.6640Grade IVMine 40.8006Grade IIMine 50.7033Grade IIIGrade I0.8735The critical value of safety gradeGrade II0.7904Grade III0.6643Grade IV0.5331It can be seen from Table4 that the safety grade of the five mine samples is ranked as follows: mine 4 > grade II (relatively safe) > mine 2 > mine 5 > grade III (moderately safe) > mine 3 > mine 1 > grade IV (generally safe). The safety grade of mine 4 is grade II and has maintained a good safety condition for a long time. The safety status of other coal mines needs to be improved. The evaluation results are consistent with the actual situation, indicating that the model is accurate for the comprehensive safety evaluation of coal mines and can be applied to guide coal mine safety production.


## 4.4.1. Analysis of Coal Mine Safety Evaluation Index

To make the results more intuitive, the weight of the coal mine safety evaluation index calculated by various methods in chapter 4.2 is visualized, as shown in Figure3.Figure 3
Weights of safety evaluation index under different methods in each mine.It can be seen from the weight curve trend of each index in Figure3 that the management factor has the greatest impact on the safety evaluation results of coal mines. According to accident causation theory [63], it can be explained that human unsafe behavior, unsafe state of equipment, and unsafe production environments will eventually lead to accidents due to the distortion of information transmission and management errors. Environmental factors and human factors also have a relatively large impact on the results of coal mine safety evaluations, which further reflects the harsh environment of coal mine production in China and the relatively weak safety awareness of coal miners. The equipment factor is less influential than other factors, but it should not be ignored. This is because a good production equipment system guarantees safe coal mine production.At the same time, secondary index factors such as efficiency of safety management, Timeliness of safety management, intact rate of the equipment, and the rate of “three violations” by personnel have a greater impact on the safety evaluation of a coal mine.


## 4.4.2. Comparison of the Results of Three Coal Mine Safety Evaluation Methods

The comprehensive evaluation scores of coal mine safety in Table3 are visualized, as shown in Figure 4. The evaluation results of 5 coal mines obtained by the three methods are compared and analyzed.Figure 4
Comprehensive evaluation scores of coal mine safety based on three methods.It can be seen from Figure4 that the comprehensive evaluation score curves of the three methods are consistent with each other. Among them, the improved composite weight-TOPSIS method and the game theory combination weight-TOPSIS method have large fluctuations in the comprehensive evaluation score curve. That is, they can clearly distinguish the pros and cons of the evaluation objects. The evaluation score curve of the FAHP method tends to be relatively stable, which is not conducive to distinguishing the strengths and weaknesses of the evaluated objects. Compared with the improved composite weight-TOPSIS method, the discrimination of comprehensive evaluation scores is greater for the game theory combination weight-TOPSIS method of five sample mines. It has the characteristics of higher scores for mines with better evaluation and lower scores for mines with poor evaluation.


## 4.4.3. Determination of Coal Mine Safety Evaluation Grade

After comparing the three methods, the results obtained by the game theory combination weight-TOPSIS method have the largest discreteness and obvious discrimination. Therefore, combined with the quantitative standards of each safety level, the safety evaluation levels of five mines are calculated, and the results are shown in Table4.Table 4
Safety evaluation grade results of each mine.
MineεiSafety evaluation gradeMine 10.5840Grade IVMine 20.7528Grade IIIMine 30.6640Grade IVMine 40.8006Grade IIMine 50.7033Grade IIIGrade I0.8735The critical value of safety gradeGrade II0.7904Grade III0.6643Grade IV0.5331It can be seen from Table4 that the safety grade of the five mine samples is ranked as follows: mine 4 > grade II (relatively safe) > mine 2 > mine 5 > grade III (moderately safe) > mine 3 > mine 1 > grade IV (generally safe). The safety grade of mine 4 is grade II and has maintained a good safety condition for a long time. The safety status of other coal mines needs to be improved. The evaluation results are consistent with the actual situation, indicating that the model is accurate for the comprehensive safety evaluation of coal mines and can be applied to guide coal mine safety production.


## 5. Discussion

Through the systematic summary of the safety evaluation of 5 mines under Zheng Coal Group, the rationality of the selected evaluation indexes for the application of coal mine safety evaluation is revealed. At the same time, the three evaluation methods are compared, and the game theory combination weight-TOPSIS method can more accurately and reasonably reflect the current quo in the process of coal mine safety production.The weights obtained by FAHP, EWM, and BP-NN are combined and weighted by using the method of game theory, so that the final weight not only takes into account the subjective experience judgment of experts but also reflects the objective law of index data [61]. While greatly reducing the negative impact of subjective consciousness and artificial randomness, it increases the scientific nature of index weighting and optimizes the TOPSIS comprehensive evaluation model [64]. Compared with the single weighting evaluation method, the game theory combination weight-TOPSIS method is more in line with the current actual situation. The evaluation results are more scientific and reasonable and have a certain value of practical promotion and application.At present, China’s coal mines need to solve the following problems to maintain a safe production level. The safety management system is inadequate and the operation mode is single [65]. The supervision and emergency system need to be improved [66]. The cultural dissemination mechanism is not yet perfect, including insufficient cultural construction, and weak safety training [67]. The production environment is harsh, with many dangerous and pollution factors in the workplace, such as gas, dust, and noise [68]. The degree of mechanization of coal mining is not enough, and the workload of miners is heavy. Miners may encounter unfair treatment at work, poor feedback and communication of fundamental rights, low levels of organizational care for miners, and serious deviations between expectations, ideals, and reality [69]. Based on this, overall measures to improve safety management in coal mines are proposed in conjunction with the evaluation results.(1)
Establish a coal mine safety production warning system. Systematic monitoring of coal mines is based on the four aspects of “man-machine-environment-management” and the scientific identification of hazard sources through comprehensive safety evaluation. When it is found that there are factors that cause the coal mine production to be in an abnormal or dangerous state, the warning system can quickly identify and find the problem. It can put forward corresponding countermeasures in time to avoid the occurrence of unsafe accidents.(2)
Formulate a perfect emergency management system. When the safety evaluation result fails to meet the requirements, the coal mine production system can become an emergency management state. Coal mine safety management personnel correct unsafe production conditions in the mine production system by implementing precontrol countermeasures.(3)
To ensure the perfection and implementation of the safety management system. The safety of coal mines depends on safety management, and the success of safety management depends on the safety management system. For different types of coal mines, management personnel should timely find the problems existing in safety management and improve the corresponding rules and regulations.(4)
Regularly conduct key inspections on the illegal operations of coal miners. Management personnel can conduct patrol inspections on coal miners through monitoring and one-to-one supervision, to timely correct violations and reduce unsafe accidents caused by personnel operation errors. Adjust the work plan with weak adaptability through communication to improve efficiency on the premise of ensuring safety.(5)
Maintain the equipment regularly. Reliability sampling inspection and equipment maintenance are carried out to reduce the impact of equipment failure on coal mine safety production. Provide the necessary support treatment to the coal seam roof to reduce the damage to equipment and miners in the roadway from mining pressure.


## 6. Conclusions and Limitations

Through example verification, the following conclusions are obtained.(1)
Considering the shortcomings of subjective and objective weighting, the advantage of the BP-NN adaptive supplementary learning mechanism is used to achieve the purpose of dynamically evaluating the safety status of coal mines. The weights obtained from FAHP, EWM, and BP-NN, are combined using the game theory combination method to get the combination weights. The game theory combination weight-TOPSIS comprehensive evaluation model is constructed.(2)
The example validation shows that the results of the game theory combination weight-TOPSIS method for safety evaluation of coal mines are consistent with those obtained by FAHP and the improved composite Weight-TOPSIS method. It has been proved that the game theory combination weight method is reasonable and feasible in the comprehensive evaluation of coal mine safety and the determination of the index weight.(3)
The improved composite weight-TOPSIS method and the game theory combination weight-TOPSIS method have a large degree of fluctuation in the comprehensive evaluation score curve of coal mine safety. In contrast, the FAHP method has a lower degree of fluctuation in the comprehensive evaluation score curve of coal mine safety. Among them, the game theory of combination weighting combines a variety of weight determination methods to form a combination weight, which is more reasonable in the comprehensive evaluation results.(4)
Compared with the improved composite weight-TOPSIS method, the game theory combination weight-TOPSIS method has a greater degree of distinction in the comprehensive evaluation of coal mine safety. This method has higher scores for mines with better evaluation and lower scores for mines with poor evaluation, to make the comprehensive evaluation results more intuitive. Therefore, the game theory combination weight-TOPSIS method has more advantages in the comprehensive evaluation of coal mine safety.(5)
Based on the results of the comprehensive safety evaluation of the five sample mines, and taking into account the actual production conditions, the corresponding coal mine safety condition improvement measures are proposed.There may be some possible limitations of this research, which can be further explored in future research:(1)
This paper only analyzes the application of five mine data subordinate to a coal mine in the game theory combination weight-TOPSIS model. There may be differences in geographical location, corporate culture, and management methods among different coal mines. Therefore, it is suggested to consider adding different coal mines for comparative analysis in future research and at the same time, improve and update the coal mine data more comprehensively and carefully.(2)
A variety of weight assignment methods are used in this paper. Although the comprehensive application of various methods makes the research results more convincing, it also makes the data processing of the paper more cumbersome. In the future, one or two methods can be improved by reducing the use of methods for future research. For example, upgrading and improving the algorithm in the process of neural network application, etc.



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*Source: 5623282-2022-10-14.xml*