## 3 Numerical Simulation
Therefore, the fuzzy set of evaluation index weight can be obtained as \(X\) = (0.20,0.20,0.15,0.15,0.15,0.15). We employed Equation (7):  
\[\left\{ \begin{array}{l}g_{i}^{*}=g_{i}(v_{i},v_{0})=\frac{1}{x}\left[\sum \limits_{k=1}^{m}\left(x_{k}\delta_{k(i)}\right)^{2}\right]^{0.5}\\ x=\frac{1}{m}\sum\limits_{k=1}^{m}x_{k}\end{array} \right. \tag{7}\]  
where \(m\) is the number of evaluation indexes; \(x\) is the average value of index weight; \(x_{k}\) is the weight value corresponding to \(k\) evaluation index; \(g_{i}^{*}\) represents the distance between the \(i\) test group and the optimal effect within the given factor level range. The smaller the \(g_{i}^{*}\) value, the higher the optimization level of the test group. When the proposed weight fuzzy set is \(X\), the range situation of \(g_{i}\) is shown as in Figure 7. The main influencing factor obtained by the comprehensive evaluation method is the elastic modulus of the backfill body and the selected optimal scheme is \(E_{S}\rho_{1}c_{3}\varphi_{1}n_{1}k_{1}\). If the decision makers adopt different evaluation index weight preferences, the results will be different, but the optimization design of backfill reinforcement parameters can still be carried out according to the method proposed in this paper. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Serial** & **Factor Level** & **Backfill Floor** & **Crown** & **Left** & **Right** & **Initial** & **Initial** \\
**Number** & **Combination** & **Displacement** & **Settlement** & **Convergence** & **Convergence** & **Lining Shaft** & **Bending** \\ \hline
16 & \(E_{4}\rho_{1}c_{4}\varphi_{2}n_{5}k_{3}\) & 0.049 & 0.245 & 0.316 & 0.289 & 0.455 & 0.107 \\
17 & \(E_{4}\rho_{2}c_{5}\varphi_{3}n_{1}k_{4}\) & 0.033 & 0.320 & 0.360 & 0.384 & 0.712 & 0.237 \\
18 & \(E_{4}\rho_{3}c_{1}\varphi_{4}n_{2}c_{5}\) & 0.492 & 0.436 & 0.744 & 0.472 & 0.123 & 0.807 \\
19 & \(E_{4}\rho_{4}\rho_{5}n_{3}k_{1}\) & 0.182 & 0.089 & 0.269 & 0.265 & 0.609 & 0.078 \\
20 & \(E_{4}\rho_{5}c_{5}\varphi_{3}n_{4}k_{3}\) & 0.314 & 0.194 & 0.237 & 0.221 & 0.199 & 0.222 \\
21 & \(E_{5}\rho_{1}c_{5}\varphi_{4}n_{3}k_{2}\) & 0 & 0.125 & 0.215 & 0.176 & 0.492 & 0.116 \\
22 & \(E_{5}\rho_{2}c_{1}\varphi_{5}n_{4}k_{3}\) & 0.174 & 0.111 & 0.248 & 0.123 & 0.211 & 0.151 \\
23 & \(E_{5}\rho_{3}c_{2}\varphi_{1}n_{5}k_{4}\) & 0.206 & 0.225 & 0.337 & 0.112 & 0 & 0.179 \\
24 & \(E_{5}\rho_{4}c_{3}\varphi_{2}n_{1}k_{5}\) & 0.219 & 0.213 & 0.424 & 0.256 & 0.312 & 0.281 \\
25 & \(E_{5}\rho_{5}c_{4}\varphi_{3}n_{2}k_{1}\) & 0.144 & 0 & 0.213 & 0.228 & 0.627 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluating Indicator** & **Primary and Secondary Factors** & **Optimal Combination** \\ \hline Backfill floor displacement & \(E>c>\rho>\varphi>k>n\) & \(E_{S}\rho_{1}c_{4}\varphi_{5}n_{4}k_{1}\) \\ Crown settlement & \(E>k>c>n>\rho>\varphi\) & \(E_{S}\rho_{1}c_{1}\varphi_{3}n_{1}k_{1}\) \\ Left convergence & \(E>k<c>\varphi>n\) & \(E_{S}\rho_{2}c_{4}\varphi_{5}n_{5}k_{1}\) \\ Right convergence & \(E>k<c>\varphi>n>\rho\) & \(E_{S}\rho_{1}c_{1}\varphi_{2}n_{1}k_{1}\) \\ Initial lining shaft & \(c>\rho>E>\rho>k>n\) & \(E_{S}\rho_{1}c_{1}\varphi_{1}n_{5}k_{5}\) \\ Initial lining bending moment & \(E>k>\varphi>\rho>c>n\) & \(E_{S}\rho_{2}c_{4}\varphi_{1}n_{3}k_{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Direct analysis results of L\({}_{25}\) (5\({}^{6}\)) standard orthogonal experiment. The strength parameter group of the reinforcement optimized using this method is defined as group 26, and the weighted deviation distances of 26 conditions are calculated at the same time.