## 3 Methodology
### Method for Identification of Main Impact Factors  
The analytic hierarchy process (AHP) [22] can be applied to multi-objective fuzzy evaluation decision-making and has now become an important tool for statistical analysis in many disciplines. AHP has the characteristics of combining qualitative and quantitative analysis. However, it also has certain limitations--determining the weights of different factors according to human-subjective factors has a greater impact and does not apply to the analysis of higher-precision decision-making [26]. Therefore, in this section, after using the AHP to initially determine the weight matrix of impact risk factors, the EWM [23] is used to further determine the weight ranking of each factor. The specific steps are shown below:  
Step 1: Modeling of hierarchical structures. To thoroughly analyze the research objectives and elucidate the interrelationships and the extent of influence of the factors within the evaluation system, it is imperative to delineate the hierarchical relationships, both upper and lower, of the evaluation indices. This delineation should be based on the attributes and the positioning of each factor within the evaluation system, ultimately resulting in a tree-diagram-like subordinate structural relationship. Step 2: Constructing judgment matrices. This paper adopts a single-level model structure. The judgment matrix can be constructed as shown in Equation (1). \[P= \begin{bmatrix}a_{11}&a_{12}&\cdots&a_{1j}\\ a_{21}&a_{22}&\cdots&a_{2j}\\ \cdots&\cdots&\cdots&\cdots\\ a_{i1}&a_{i2}&\cdots&a_{ij}\end{bmatrix}  \tag{1}\]  
where \(a_{i}\), \(a_{j}\) (\(i,j=1\), 2, 3, \(\ldots\), \(n\)) are the indicator factors for the evaluation. The meaning of \(a_{ij}\) is \(a_{i}\) relative to the relative influence or importance of \(a_{j}\), from \(a_{ij}\). Within the hierarchical evaluation system, the degree of influence or importance of all factors at the same level is assessed. Furthermore, based on the criteria for value assignment in the consistency matrix (Table 1), the individual evaluation factors are quantified. This quantification leads to the formation of the final judgment matrix, which is utilized for evaluating the influence factors. Figure 3: Flow chart of the detailed calculation of the SSPs and risk assessment. Step 3: Compute the weight vector. Utilizing the judgment matrix, compute the eigenvector corresponding to the largest eigenvalue as shown in Equation (2). Normalization is then performed to obtain the weight ordering of each factor. \[Pw=\lambda_{\text{max}}w \tag{2}\]  
where \(\omega\) is the eigenvector and \(\lambda_{\text{max}}\) is the corresponding largest eigenvalue. Step 4: Consistency check. To verify the accuracy of the weighting coefficients, the results should be examined using the consistency ratio \(CR\) (Equation (3)). The judgment matrix is deemed to have acceptable consistency and passes the consistency test if CR < 0.1. \[CR=\frac{CI}{RI}=\frac{\lambda_{\text{max}}-n}{(n-1)RI} \tag{3}\]  
where \(n\) denotes the order of the judgment matrix. \(CI\) is a consistency indicator. \(RI\) denotes the random consistency index, and the values are shown in Table 2.  
After the initial determination of the weights of the rockburst risk factors, the EWM was used to determine the weight ordering steps of the factors as follows:  
Step 5: Construct the original matrix. Assuming that there are \(i\) evaluation objects and \(j\) evaluation indicators, the original matrix is as follows:  
\[X= \begin{bmatrix}x_{11}&x_{12}&\cdots&x_{1j}\\ x_{21}&x_{22}&\cdots&x_{2j}\\ \cdots&\cdots&\cdots&\cdots\\ x_{i1}&x_{i2}&\cdots&x_{ij}\end{bmatrix}  \tag{4}\]  
where \(x_{ij}\) is the weight of the \(j\)-th indicator for the \(i\)-th element in the judgment matrix. Step 6: Non-negativization of data. Normalization is required when the evaluation indicators are inversely proportional and moderate. Additionally, data leveling must be performed to prevent the meaninglessness of the logarithm during entropy value calculation.