## 4 Results  
### Landslide Hazard  
#### 4.1.1 Results of the AHP Model  
According to Equations (4) and (5), the values of the CI, RI, and CR are 0.027, 1.490, and 0.018, respectively. This indicates that the results of the judgment matrix shown in Table 5 meet the requirements of the AHP model. Next, the obtained weight of each predisposing factor was input into Equation (6) to calculate the LHI, as shown in Equation (10). Then, we normalized the LHI, and its value range was from 0 to 1. Finally, the landslide hazard maps of the AHP model were generated using the GIS software. Based on the natural breakpoint method, we highlighted the characteristics of different levels of LHIs and classified the  
Figure 6: Vulnerability factors of the study area: (**a**) population density; (**b**) GDP density; (**c**) road density; (**d**) mine density; (**e**) land use.  
generated LHIs into five grades (Figure 7a,b): very low, low, moderate, high, and very high. Similarly, the other LHI results obtained in this study were also classified by the natural breakpoint method.  
\[\begin{array}{c}LHI_{AHP}=0.216\times PF_{1}+0.050\times PF_{2}+0.162\times PF_{3 }+0.116\times PF_{4}+0.079\times PF_{5}+\\ 0.162\times PF_{6}+0.050\times PF_{7}+0.031\times PF_{8}+0.019\times PF_{9}+0.116 \times PF_{10}\end{array} \tag{10}\]  
where \(PF_{1}\) to \(PF_{10}\) are the FR values of the corresponding predisposing factors in Table 3.  
Figure 7 shows that the results of the FR-AHP model (Figure 7a) and the DFR-AHP model (Figure 7b) are relatively close. Based on the FR-RF model (Figure 7a), the zones with very low (0-0.15), low (0.15-0.29), moderate (0.29-0.43), high (0.43-0.61), and very high (0.61-1) landslide hazards cover 21.96%, 31.15%, 27.36%, 12.79%, and 6.75% of the entire study area, respectively. Moreover, in the landslide hazard map generated by the DFR-AHP model (Figure 7b), the proportions of very low (0-0.13), low (0.13-0.26), moderate (0.26-0.39), high (0.39-0.58), and very high (0.58-1) landslide hazard zones are 20.85%, 30.52%, 27.45%, 13.72%, and 7.46%, respectively. Meanwhile, zones with very high and high landslide hazards are mainly distributed between Aoyitake and Bulunkou. However, compared with the FR-AHP model, the landslide hazard map obtained by the DFR-AHP model clearly displays that there are more zones with very high and high landslide hazards between Aoyitake and Bulunkou.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Predisposing Factor** & \(PF_{1}\) & \(PF_{2}\) & \(PF_{3}\) & \(PF_{4}\) & \(PF_{5}\) & \(PF_{6}\) & \(PF_{7}\) & \(PF_{8}\) & \(PF_{9}\) & \(PF_{10}\) & **Weight** \\ \hline \(PF_{1}\) & 1 & & & & & & & & & 0.216 \\ \(PF_{2}\) & 1/5 & 1 & & & & & & & 0.050 \\ \(PF_{3}\) & 1/2 & 4 & 1 & & & & & & 0.162 \\ \(PF_{4}\) & 1/3 & 3 & 1/2 & 1 & & & & & 0.116 \\ \(PF_{5}\) & 1/4 & 2 & 1/3 & 1/2 & 1 & & & & 0.079 \\ \(PF_{6}\) & 1/2 & 4 & 1 & 2 & 3 & 1 & & & 0.162 \\ \(PF_{7}\) & 1/5 & 1 & 1/4 & 1/3 & 1/2 & 1/4 & 1 & & 0.050 \\ \(PF_{8}\) & 1/6 & 1/2 & 1/5 & 1/4 & 1/3 & 1/5 & 1/2 & 1 & & 0.031 \\ \(PF_{9}\) & 1/7 & 1/3 & 1/6 & 1/5 & 1/4 & 1/6 & 1/3 & 1/2 & 1 & & 0.019 \\ \(PF_{10}\) & 1/3 & 3 & 1/2 & 1 & 2 & 1/2 & 3 & 4 & 5 & 1 & 0.116 \\ \hline \end{tabular}
\end{table}
Table 5: The judgment matrix and weight values of the predisposing factors in the AHP model.  
Figure 7: Landslide hazard maps based on different LHA models: (**a**) FR-AHP model; (**b**) DFR-AHP model; (**c**) FR-RF model; (**d**) DFR-RF model.