## 2 Modeling of a Multi-Dimensional Evaluation Indicator System
### Methodology for Screening Key Evaluation Indicators
To avoid the problem of there being too large of a difference between the scale of each evaluation indicator and the data scale standard, the data were first normalized via dimensionless normalization. The data matrix was established using 1200 sets of sample indicator datasets, constituting a matrix of dimensions 1200 \(\times\) 19 (S1-S19), as shown in Equation (2). \[\widetilde{S}=\left[ \begin{array}{cccc}a_{1S_{1}}&a_{1S_{2}}&\cdots&a_{1S_{19 }}\\ a_{2S_{1}}&a_{2S_{2}}&\cdots&a_{2S_{19}}\\ a_{iS_{1}}&\cdots&a_{ij}&a_{iS_{19}}\\ \vdots&\vdots&\ddots&\vdots\\ a_{1200S_{1}}&a_{1200S_{2}}&\cdots&a_{1200S_{19}}\end{array} \right] \tag{2}\]  
\[\overline{a}=\frac{\sum\limits_{i=1}^{1200}a_{ij}}{1200} \tag{3}\]  
\[b_{ij}=\frac{a_{ij}}{\overline{a}_{j}} \tag{4}\]  
Matrix \(B\) after dimensionless normalization is shown in Equation (5). \[B=\left[ \begin{array}{cccc}b_{1S_{1}}&b_{1S_{2}}&\cdots&b_{1S_{19}}\\ b_{2S_{1}}&b_{2S_{2}}&\cdots&b_{2S_{19}}\\ \vdots&\vdots&\ddots&\vdots\\ b_{1200S_{1}}&b_{1200S_{2}}&\cdots&b_{1200S_{19}}\end{array} \right] \tag{5}\]  
For the 1200 sample datasets categorized by risk level, the output label, \(d_{i}\), is denoted as 1 for slopes at the alarm level and 0 for slopes at other levels. The corresponding Boolean result matrix is represented as \(D\), as illustrated in Equation (6). \[D=\left[d_{1}\quad d_{2}\quad\cdots\quad d_{1200}\right] \tag{6}\]  
We can determine the gray relation coefficients between each evaluation indicator and landslides based on matrix \(B\) and matrix \(D\), as shown in Equation (7). \[\xi_{ij}=\frac{\min\limits_{ \begin{array}{c}1\leq i\leq 1200\\ 1\leq j\leq 19\end{array} }\left|d_{j}-b_{ij}\right|+\rho\max\limits_{ \begin{array}{c}1\leq i\leq 1200\\ 1\leq j\leq 19\end{array} }\left|d_{j}-b_{ij}\right|\\ \frac{1\leq j\leq 19}{\left|d_{j}-b_{ij}\right|+\rho\max\limits_{ \begin{array}{c}1\leq i\leq 1200\\ 1\leq j\leq 19\end{array} }\left|d_{j}-b_{ij}\right|} \tag{7}\]where \(\rho\) is the resolution coefficient. The smaller \(\rho\) is, the greater the resolution, and \(0<\rho<1\); in this study, 0.5 was taken as the value. Thus, the gray relation coefficient, \(r_{i}\), is shown in Equation (8). \[r_{i}=\frac{1}{1200}\sum_{i=1}^{1200}\xi_{ij} \tag{8}\]  
The calculated weights of each indicator in relation to the impact of landslides are shown in descending order in Figure 3. Larger values represent a higher impact of the indicator on landslides. Figure 3 shows that the precipitation and soil moisture condition indicators have a greater weight on the influence of slope stability, and there is a clear disconnect from the other indicators. Combined with the results of Pearson correlation coefficient analysis, the S\({}_{1}\), S\({}_{4}\), S\({}_{5}\), S\({}_{8}\), S\({}_{9}\), S\({}_{12}\), S\({}_{13}\), S\({}_{14}\), S\({}_{17}\), and S\({}_{18}\) indicators were excluded, and 10 indicators (slope, curvature, temperature, daily precipitation, vegetation coverage, NDVI, soil shear strength, soil moisture content, reservoir water level, and slope deformation) were finally identified as the key indicators for slope risk assessment, which were renumbered F\({}_{1}\)-F\({}_{10}\) for the convenience of the subsequent analysis, as shown in Table 1.