## 4 Results and Discussion
### The Calculation Process of the Improved VFS Method
\right] \tag{39}\]  
where the first row is the points M of \(\sigma_{\theta}/\sigma_{c}\) to four levels and the remaining rows represent \(\sigma_{c}/\sigma_{t}\) and \(w_{et}\). \[\left[c_{ij},d_{ij}\right]=\left[ \begin{array}{cccc}[0.1,\ 0.5]&[0.1,\ 0.7]&[0.3,\ 0.9]&[0.5,\ 0.9]\\ [52.57,\ 26.7]&[52.57,\ 14.5]&[40,\ 1.57]&[26.7,\ 1.57]\\ [0.5,\ 3.5]&[0.5,\ 5]&[2,\ 6.5]&[3.5,\ 6.5]\end{array} \right] \tag{40}\]  
where the first row is the extended interval of \(\sigma_{\theta}/\sigma_{c}\) to four levels and the remaining rows represent \(\sigma_{c}/\sigma_{t}\) and \(w_{et}\). 2. RMD matrix of indicators  
In this paper, the rockburst case in Tianshengqiao II hydropower station is selected to illustrate the calculation process of RMD. The eigenvalues of \(\sigma_{\theta}/\sigma_{c}\), \(\sigma_{c}/\sigma_{t}\), and the \(w_{et}\) indicator in Tianshengqiao II hydropower station are 0.34, 23.97, and 6.60, respectively. The eigenvalue \((x_{1}=0.34)\) of \(\sigma_{\theta}/\sigma_{c}\) is located in the interval of level II. For level II, the VFS model parameters (c, a, M, b, d) are 0.1, 0.3, 0.4, 0.5, and 0.7, respectively. From this, it can be seen that the eigenvalue \(x_{1}\) is between a (0.3) and M (0.4). Taking these parameters into Equation (5), the RMD value of level II can be calculated to be 0.7. Similarly, for level I, the VFS model parameters (c, a, M, b, d) are 0.1, 0.1, 0.1, 0.3, and 0.5, respectively, and \(x_{1}\) is between b (0.3) and d (0.5). The RMD of level I can be calculated as 0.4 by introducing the above parameters into Equation (8). According to the characteristics described in Equation (26), the RMD is 0.1 for level III and is 0 for level IV. For \(\sigma_{c}/\sigma_{t}\), the eigenvalue \((x_{2}=23.97)\) is located in the interval of level III. The VFS model parameters (c, a, M, b, d) of level III are 40, 26.7, 20.6, 14.5, and 1.57, respectively. Based on this, the eigenvalue \(x_{2}\) belongs to the interval \([a,M]\). Inserting the above parameters into Equation (5), the RMD for level III is 0.724. Similarly, the VFS model parameters (c, a, M, b, d) of level IV are 26.7, 14.7, 1.5, 1.5, and 1.57, respectively. Therefore, \(x_{2}\) is between c and a and the RMD for level IV can be calculated by introducing the above parameters into Equation (6) with a value of 0.112. The RMDs of level II and level I are 0.388 and 0, respectively, based on characteristic formula of Equation (26). Figure 9: Polynomial regression of the quantitative boundary eigenvalue \((L_{min}\)_or \(L_{max})\) for all indicators. As for \(w_{et}\), the eigenvalue \((x_{3}=6.6)\) is greater than the pseudo-boundary value 6.5 of level IV. Equation (29) shows that RMD is equal to 1 for level IV and to 0 for other levels. Therefore, the RMD matrix of these three indicators in Tianshengqiao II hydropower station can be expressed as follows:  
\[u_{ij}(x)=\left[ \begin{array}{cccc}0.400&0.700&0.100&0.000\\ 0.000&0.388&0.724&0.112\\ 0.000&0.000&0.000&1.000\end{array} \right] \tag{41}\]  
Similarly, the RMD matrix of all rockburst cases can be obtained by repeating the above process. 3. The Initialized SRMD The comprehensive evaluation model of Equation (10) can transform RMD into SRMD, but the weight of each index and model parameters \(\alpha\) and \(p\) should be determined first. In this paper, \(\alpha=2\) and \(p=1\) fuzzy optimization models are selected and eight different weight assignments are obtained from the references in Table 1. Based on the above analysis, combined with RMDs and eight weight assignment values, the initial SRMD can be calculated through Equation (10). Then, the initial SRMD is introduced into Equation (17) to obtain the level eigenvalue H, as shown in Figure 10a. 4. The Optimized SRMD In order to optimize the SRMD, a three-layer BP neural network is established. The nodes of the input layer, the hidden layer, and the output layer are 4, 5, and 4, respectively.