## 3 Results and Validation
### Application of the Integrated ANFIS Methods  
To construct the training and verification sets, the same number of 315 non-landside grid cells were first randomly selected using ArcGIS. Then, 70% landslide and non-landside grid cells were used for model building, and the remaining landslide and non-landside grid cells were used for assessing the prediction performance [125; 126; 127; 128]. It is better to noted that in this stage, only the weights of each factors by SWARA method is considered for integration. Once the training and verification sets were constructed, the SWARA, SWARA-ANFIS, SWARA-ANFIS-PSO, SWARA-ANFIS-WOA and SWARA-ANFIS-GWO methods were used to predict landslide susceptibilities for Anyuan County. In the proposed framework, the meta-heuristic algorithms were programmed using MATLAB software, and the parameters of membership functions were optimized [129; 130; 131; 132]. The GWO, WOA, and PSO algorithms enhance the prediction accuracy of ANFIS. Firstly, a given weight is assigned to each class and each influencing factor, and then, an output is computed. Consequently, each weighted class is considered as input data for ANFIS to find the weight of each factor. In the next stage, GWO, WOA, and PSO based on ANFIS are implemented to optimize the obtained weight of ANFIS in the earlier stage. Figure 9 shows a mathematic example that how these algorithms run and lead to enhance the power prediction of ANFIS algorithm. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Influencing Factors** & **CIAV** & **Aj** & **wj = (W(j\(-\)1))/Aj** & **Weight wj/Sigma wj** \\ \hline
**Slope angle (o)** & & 1.000 & 1.000 & 0.105 \\
**Rainfall** & 0.05 & 1.050 & 0.952 & 0.100 \\
**Lithology** & 0.1 & 1.100 & 0.866 & 0.091 \\
**Soil** & 0.06 & 1.060 & 0.817 & 0.086 \\
**Land use** & 0.06 & 1.060 & 0.771 & 0.081 \\ NDVI & 0.07 & 1.070 & 0.720 & 0.076 \\
**Distance to Rivers (m)** & 0.07 & 1.070 & 0.673 & 0.071 \\
**Distance to faults (m)** & 0.03 & 1.030 & 0.653 & 0.069 \\
**TWI** & 0.05 & 1.050 & 0.622 & 0.066 \\
**SPI** & 0.08 & 1.080 & 0.576 & 0.061 \\
**Altitude** & 0.1 & 1.100 & 0.524 & 0.055 \\
**STI** & 0.1 & 1.100 & 0.476 & 0.050 \\
**Aspect** & 0.3 & 1.300 & 0.366 & 0.039 \\
**Profile curvature** & 0.3 & 1.300 & 0.282 & 0.030 \\
**Plan curvature** & 0.5 & 1.500 & 0.188 & 0.020 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculate weight of influencing factors by the SWARA algorithm. Figure 9: An example scheme of modelling producer of evolutionary optimization algorithms. Figures 10-12 show the accuracy of training and verification processes for the SWARA-ANFIS-GWO and SWARA-ANFIS-WOA, and SWARA-ANFIS-PSO methods, respectively. The RMSE was selected to assess the prediction performance of the three methods in both training and verification phases. The results demonstrate that the RMSE for SWARA-ANFIS-PSO, SWARA-ANFIS-WOA and SWARA-ANFIS-GWO methods were 0.099, 0.1, and 0.099 in the training phase and 0.120, 0.11, and 0.1 in the verification phase, respectively. Meanwhile, GWO can optimize the better parameters of membership functions than that of WOA in both the training and verification phase. To evaluate the efficiency of the two methods, the cost function values are calculated and plotted versus each iteration of convergence graph for the three proposed methods, as shown in Figure 13. The cost function values of ANFIS-GWO, SWARA-ANFIS-WOA and SWARA-ANFIS-PSO are stable after 17, 362, and 49 iterations, which validates that SWARA-ANFIS-GWO is more efficient than SWARA-ANFIS-WOA and SWARA-ANFIS-PSO. Figure 10: The SWARA-ANFIS-WOA method. (**a**) Target and outputs for the training set; (**b**) target and outputs for the verification set; (**c**) MSE and RMSE for the training set; (**d**) frequency errors for the verification set; (**e**) MSE and RMSE for the verification set; (**f**) frequency errors for the verification set. Figure 11: The SWARA-ANFIS-GWO method.