Safety Risk Assessment of a Pb-Zn Mine Based on Fuzzy-Grey Correlation Analysis

: Improving safety management and risk evaluation methods is important for the global mining industry, which is the backbone of the industrial development of our society. To prevent any accidental loss or harm to human life and property, a safety risk assessment method is needed to perform the continuous risk assessment of mines. Based on the requirements of mine safety evaluation, this paper proposes the Pb-Zn mine safety risk evaluation model based on the fuzzy-grey correlation analysis method. The model is compared with the risk assessment model based on the fuzzy TOPSIS method. Through the experiments, our results demonstrate that the proposed fuzzy-grey correlation model is more sensitive to risk and has less e ﬀ ect on the evaluation results under di ﬀ erent scoring attitudes (cautious, rational, and relaxed). M.W. and R.D.; formal analysis, G.D. and X.X.; investigation, G.D., W.W., X.X., and M.W.; resources, G.D., W.W., and X.X.; data curation, G.D., W.W. and X.X.; writing, original draft preparation, G.D., W.W., and X.X.; writing, review and editing, M.W. and R.D.; visualization, R.D.; supervision, W.W. authors


Introduction
Mining ensures the supply of the required material as the foundation for the industrial development of our society, but also is the cause of many accidents and deaths worldwide [1]. Therefore, mine safety is very important to ensure the sustainable development of the global economy [2]. To prevent mine accidents, mine safety risk should be assessed and properly managed. Safety risk management [3], the evaluation and mitigation of the safety risks of the consequences of hazards, has gradually developed into an independent research discipline, because of the continuous development of risk analysis and control theory. Improving the level of safety management has become an urgent real requirement for business enterprises since the emergence of globalization and the introduction of corporate social responsibility. Researchers have done many experiments using fuzzy logic [4] in the field of risk assessment, including hazardous industrial installations [5,6], the aluminum industry [7], hydropower stations [8], shipping routes [9], supply chains [10], railway transportation systems [11], construction projects and green buildings [12,13], and occupational health and safety [14,15].

Preliminaries
In the following, we provide the definition of the related concepts of fuzzy numbers. Definition 1. ( [50]). The normal convex fuzzy sets on the real number field R are called the fuzzy numbers; the regular closed convex fuzzy sets are called the closed fuzzy numbers; the regular bounded closed convex fuzzy sets are called the bounded closed fuzzy numbers. If A is the fuzzy number and A 1 = 1−cut is a single point set, that is A 1 = {x 0 }, then A is a strictly fuzzy number. Definition 2. ( [51]). Let A be a fuzzy number; A is set Supp A = (a 1 , a 2 ), a 1 > a 2 ; if: • a 1 ≥ 0, set A to a positive fuzzy number, indicated by A > 0; • a 2 ≤ 0, set A to a negative fuzzy number, indicated by A < 0; • a 1 < 0, a 2 > 0, set A to a zero fuzzy number, indicated by A ≥ 0 or A ≤ 0; • a 1 < 0, a 2 > 0 and µ A (0) = 1, set A to a zero fuzzy number, indicated by A = 0.
Definition 3. ( [52]). Let any fuzzy numbers be represented by a pair of functions and any fuzzy number be set b = (b L (r), b R (r)) to satisfy for ∀r, 0 < r < 1: (1) b L (r) is a bounded left continuous non-decreasing function; (2) b R (r) is a bounded right continuous non-increasing function; (3) b L (r) ≤ b R (r). Then, the fuzzy number b = (b L (r), b R (r)) is a function pair.
Definition 4. Let fuzzy number A have membership degree: Let us call A the triangular fuzzy number denoted by A = (a, b, c).

Definition 5.
( [53]). Let E be a fuzzy set on R; the membership function denoted by E(x), x ∈ R. If E(x), satisfies these properties: (1) E(0) = 1; (2) E(x) is a monotonically increasing left continuous function in the interval −1, 0) and in the interval 0, 1 is a monotonically decreasing right continuous function; Then, the fuzzy set E is a fuzzy structured element on R.

Definition 7.
Let fuzzy sets E have membership functions: Call it a triangular fuzzy structured element.

Fuzzy-Grey Relation Ranking Method Based on the Structured Element Method
The fuzzy-grey relation ranking method based on the structured element method is described as follows: Step 1: Fuzzy structure meta-representation of the fuzzy decision matrix. The original data fuzzy matrix X is constructed by the known risk values.
Electronics 2020, 9, 130 4 of 20 where x ij (i = 1, 2, · · · , m, j = 1, 2, · · · , n) represents the risk value RM ij (fuzzy number) of the evaluation object i in the evaluation index j. Let E be a regular fuzzy structured element, and use the structured element to represent the fuzzy number: where f x ij (x), x ∈ [−1, 1] is a monotonically increasing function.
Step 2: Assign weight to the fuzzy decision matrix, then the fuzzy decision matrix would be: Among them v ij = w j x ij = g j (E) f x ij (E),i = 1, 2, · · · , m, j = 1, 2, · · · , n. w j = g j (E) is the fuzzy weight, and g j (x), x ∈ [−1, 1] is a monotonically increasing function. For the convenience of description, Step 3: Determine the ideal object v 0 that is the optimal index set; denoted by v 0 = ( v 01 , v 02 , · · · , v 0n ). Usually, the optimal value of the jth index in all the subjects is taken as the value of v 0 j .
x v ij , the jth index has a positive impact mi i n v ij , the jth index has a negative impact (6) Correspondingly, define the ideal function of each index: x f ij , the jth index has a positive impact mi i n f ij , the jth index has a negative impact (7) Here, x ∈ [−1, 1], j = 1, 2, · · · , n. When RM selects the [0 − 1] fuzzy scale, the range of RM is [0, 3], and the optimal index is defined as v 0 = ( v 01 , v 02 , · · · , v 0n ) = (0, 0, · · · , 0). At this time, f 1 j = 0, j = 1, 2, · · · , n. When RM selects the 1 9 − 9 fuzzy scale, the range of RM is 1 Step 4: Calculate the distance between fuzzy numbers based on structured elements. Let E(x), x ∈ [−1, 1] be a membership function of structured element E. The fuzzy number represented by the structure element is: A = f (E) and B = g(E). The fuzzy distance D A, B [54] between A and B is: According to the definition of the fuzzy distance, the distance between the jth index of the evaluation object i and the jth index of the ideal object is: Electronics 2020, 9, 130 5 of 20 When v ij = f ij (E) is the triangular fuzzy number, it is represented by (a, b, c). E is the triangular fuzzy element structure. Its linear function of the structured elements is: The distance between the jth index of the evaluation object i and and the jth index of the ideal object is: When f 1 j (x) is constant, then: Step 5: Calculate the elements in the correlation coefficient matrix β between the evaluation object i and the ideal object: Similarly, ρ is the resolution coefficient, and its specific value can be selected according to the principle of "fully reflecting the integrity of the correlation and having the anti-interference effect" [55]. Take ρ = 0.5 for calculation.
Each element in the matrix C of the correlation coefficient between the object i and the ideal object is evaluated: Here, w j is the fuzzy weight of the jth index. Sorted by the degree of relevance, the larger the C i value, the higher the corresponding mine safety.

Fuzzy-Grey Correlation Ranking Method Based on the Structured Element Method
The traditional grey relation analyzes the similarity between the evaluation object and the reference object. In the following, the reference object is exchanged with the evaluated object to achieve the level division of the evaluation object based on the fuzzy structure meta distance. The specific steps are as follows: Step 1: Fuzzy structure meta-representation of fuzzy decision matrix. The original data fuzzy matrix X is constructed by the known risk values as follows: where x ij (i = 1, 2, · · · , m, j = 1, 2, · · · , n) represents the risk value RM ij (fuzzy number) of the evaluation object i in the evaluation index j. Let E be a regular fuzzy structured element, and use the structured element to represent the fuzzy number: x ij = f x ij (E) (16) where f x ij (x), x ∈ [−1, 1] is a monotonically increasing function.
Step 2: Assign the weight to the fuzzy decision matrix, then the matrix would be: Step 3: Determine the p level standard matrix corresponding to n indicators: T p is the jth index of the k level evaluation of the standard value (k = 1, 2, · · · , p, j = 1, 2, · · · , n) and is also expressed by a fuzzy number. If the RM evaluation selects the [0 − 1] fuzzy scale, the range of RM is [0, 3], and the standard value of the kth stage may be: here k = 1, 2, · · · , p, is the standard value of the evaluation level and is the value with the largest degree of membership.
Step 5: Calculate the distance between the jth index of the evaluation object i and the jth index of each level in the standard matrix: Here, D i v ij , t * k j is a definite number. When v ij = f ij (E) is the triangular fuzzy number (here, it is represented by (a, b, c)), take E as the triangular fuzzy element structure; the linear function of its structured element is: Electronics 2020, 9, 130 7 of 20 The distance between the jth index of the evaluation object i and the jth index of the ideal object is: When t * k j is constant, then: is constant k = 1, 2, · · · , p.
Step 6: Calculate the correlation coefficient matrix β i between each index of evaluation object i and the standard value of each level of evaluation: Each of these elements: Similarly, take ρ = 0.5 for calculation. The correlation coefficient matrix C i between the evaluation object i and the evaluation level: Each of these elements: Similarly, w j is the fuzzy weight of the jth index. Sorted by the degree of correlation, the maximum value of C ik , the corresponding mine i has a safety level of k. This completes the mine safety assessment.

Index and Weight Data for Application Analysis of the Comprehensive Risk Evaluation Model
Referring to the mine safety risk assessment index given in [56], the Pb-Zn mine safety indicators are given in Table 1. In the design of the simulation experiment, the evaluation results are compared with the method used in [36].
In this paper, three groups of the Pb-Zn mines are scored by a group of experts. The numbers a, b, and c are the three elements of the triangular fuzzy number. The data quality control here is mainly conducted by manual identification. The original data of fuzzy risk values assessed by the experts are shown in Table 2. Million tons of ore production flood alarm rate C42 Million tons of ore fire alarm rate C43 Tons of ore hit the ground pressure alarm rate C44 Occupational health management B33 The proportion of occupational patients C45 Emergency management B34 "Safe hedging six systems" complete rate C46 In the calculation of the fuzzy weights, we used the comprehensive fuzzy weight based on the scoring attitude as in [56]. In the simulation experiment, we combined the fuzzy weight calculated by different weighting methods with different scoring attitudes to evaluate the safety risk assessment. The model was verified by simulation; the comprehensive weight of the maximum eigenvalue method and entropy weight, the comprehensive weight of the least squares method and the entropy weight, the comprehensive weight of the sum method and the entropy weight, the comprehensive weight of the product method and the entropy weight were the four comprehensive weights CW1-CW4, which are shown in Table 3. The weights for cautious, rational, and relaxed attitude are summarized in Figure 1 (only the 20 largest weights are shown for each group). The largest comprehensive weights were certified staff ratio C13 for relaxed attitude and "three violations" incidence C16 for cautious and rational attitude. This means that the factors of "certified staff" (which is related to the competences and qualifications of the personnel) and "three violations" (which is related to insecure behavior of the personnel) have the largest impact on the security assessment of the mine. The weights for cautious, rational, and relaxed attitude are summarized in Figure 1 (only the 20 largest weights are shown for each group). The largest comprehensive weights were certified staff ratio C13 for relaxed attitude and "three violations" incidence C16 for cautious and rational attitude. This means that the factors of "certified staff" (which is related to the competences and qualifications of the personnel) and "three violations" (which is related to insecure behavior of the personnel) have the largest impact on the security assessment of the mine.  Similarly, the safety of the mine was also categorized into seven levels, as presented in Table 4, in order to conduct the contrast tests.

Results of Fuzzy-Grey Correlation Risk Rating Assessment
To verify the validity of the fuzzy-grey correlation risk assessment model proposed here, the eigenvalue method based on the cautious attitude, rational attitude, and relaxed attitude for the comprehensive weight of the maximum eigenvalue method and entropy weight (CW1), the comprehensive weight of the least squares method and the entropy weight (CW2), the comprehensive weight of the sum method and the entropy weight (CW3), the comprehensive weight of the product method and the entropy weight (CW4) were used. The security risks under the four comprehensive weights were evaluated and compared with the results in [36]. The detailed experimental data are shown in Tables 5-7.

Fuzzy-Grey Correlation Risk Rating Based on Cautious Comprehensive Weight
According to the results of the simulation presented in Table 5, the fuzzy-TOPSIS model proposed in [56] was applied under the four kinds of comprehensive weights of the cautious scoring attitude. The results of the expert group assessment (represented in Figure 2) showed that the comprehensive risk level of the three mines was slightly lower, in which Mine 2 and Mine 3 had comprehensive risk ratings each of medium. By using the fuzzy-grey correlation method studied in this paper, the results of the expert group were as follows: the risk level of Mine 1 was lower, and the risk levels of Mine 2 and Mine 3 were medium. From the simulation, the results demonstrated that the proposed model was more sensitive to security risks.

Fuzzy TOPSIS Risk Rating Based on Rational Comprehensive Weight
According to the results of the simulation presented in Table 6, the proposed model was applied under the four kinds of comprehensive weights of the rational scoring attitude. The results (represented in Figure 3) showed that the comprehensive risk level of Mine 1 was lower, and the

Fuzzy TOPSIS Risk Rating Based on Rational Comprehensive Weight
According to the results of the simulation presented in Table 6, the proposed model was applied under the four kinds of comprehensive weights of the rational scoring attitude. The results (represented in Figure 3) showed that the comprehensive risk level of Mine 1 was lower, and the comprehensive risk levels of Mine 2 and Mine 3 were slightly lower.
By using the fuzzy-grey correlation method, the results of the expert group were as follows: the risk level of Mine 1 was lower, and the risk levels of Mine 2 and Mine 3 were medium. The simulation results showed that the proposed model was more sensitive to security risks.  By using the fuzzy-grey correlation method, the results of the expert group were as follows: the risk level of Mine 1 was lower, and the risk levels of Mine 2 and Mine 3 were medium. The simulation results showed that the proposed model was more sensitive to security risks.

Fuzzy TOPSIS Risk Rating Based on Relaxed Comprehensive Weight
According to the results of the simulation in Table 7, the proposed model was applied under the four kinds of comprehensive weights of the relaxed scoring attitude. The result (represented in

Fuzzy TOPSIS Risk Rating Based on Relaxed Comprehensive Weight
According to the results of the simulation in Table 7, the proposed model was applied under the four kinds of comprehensive weights of the relaxed scoring attitude. The result (represented in Figure 4) showed that the comprehensive risk level of Mine 1 was extremely low, and the comprehensive risk levels of Mine 2 and Mine 3 were comparatively lower, for which each of mines was rated extremely low.

Discussion
The model proposed in this paper demonstrated three advantages following from the results of the three sets of comparative experiments. 1 The proposed model was more sensitive to risk because the overall risk rating was generally one level higher. 2 The proposed model had little change in rating results under different scoring attitudes, so different scoring attitudes had less influence on the fuzzy-grey correlation model. 3 The proposed model did not distinguish the judgment of some adjacent ranks, because there was no strict limit to the risk assessment.
In addition, the inconsistency between the indexes, such as some indexes having higher risk levels and some indexes having lower risk levels, and the results of the comprehensive analysis may have had a small degree of discrimination. Based on the analysis of the correlation value in the table, the degree of correlation between some of the adjacent level difference was very small; such as the By using the fuzzy-grey correlation method analyzed in this paper, the results of the expert group were as follows: the risk level of Mine 1 was lower, and the risk levels of Mine 2 and Mine 3 were slightly lower. From the simulation results, we can see that the proposed model was more sensitive to security risks.

Discussion
The model proposed in this paper demonstrated three advantages following from the results of the three sets of comparative experiments.

1.
The proposed model was more sensitive to risk because the overall risk rating was generally one level higher. 2.
The proposed model had little change in rating results under different scoring attitudes, so different scoring attitudes had less influence on the fuzzy-grey correlation model. 3.
The proposed model did not distinguish the judgment of some adjacent ranks, because there was no strict limit to the risk assessment.
In addition, the inconsistency between the indexes, such as some indexes having higher risk levels and some indexes having lower risk levels, and the results of the comprehensive analysis may have had a small degree of discrimination. Based on the analysis of the correlation value in the table, the degree of correlation between some of the adjacent level difference was very small; such as the relaxed attitude Comprehensive Weight 3 had a lower level of correlation degree of 0.7814 and a medium level of correlation degree of 0.7737.
The approach presented in this paper had similarities to other risk assessment methods based on fuzzy logic such as presented in [57][58][59]. However, the latter methods required a much larger number of fuzzy rules to be constructed and evaluated as compared to the method presented in this paper.

Conclusions
In this paper, a mine safety risk ranking and grading evaluation model that was based on the fuzzy-grey correlation method was proposed. We compared this model with the fuzzy TOPSIS risk assessment model based on the cautious, rational, and relaxed scoring attitudes. Through actual analysis, we found that the proposed model was more sensitive to risk than the fuzzy TOPSIS risk assessment model in three different situations. Our results demonstrated that the risk analysis model proposed in this paper could be successfully applied to the evaluation of mine safety. The proposed model had little change in rating results under the three different scoring attitudes, so different scoring attitudes had less impact on the results of the proposed model.