*4.4. Accuracy Validation*

A review of the literature has shown that the receiver operating characteristic (ROC) curve is a popular method to evaluate the goodness of fit for classification [1,4–7]. The area under this curve (AUC) is adopted to measure the generalization performance of the LSM model. The value of AUC usually ranges between 0.5 to 1.0. A higher AUC value, closer to 1.0, indicates a better performance of the classification model.

$$\text{TPR} = \frac{\text{TP}}{\text{TP} + \text{FN}} \tag{19}$$

$$\text{FPR} = \frac{\text{FP}}{\text{FP} + \text{TN}} \tag{20}$$

The first step in performing the ROC analysis was to construct the validation dataset, which contained both landslide and non-landslide events. For this study, 425 known landslides were used for validation. Additionally, 425 non-landslides were randomly chosen for validation within the study area. Then, by setting di fferent threshold LSI values, the dataset was separated into four groups according to the actual label and precited label. As shown in Table 3, the four groups were true positive (TP), true negative (TN), false positive (FP), and false-negative (FN) events. After that, two indexes were employed; one was the true positive rate (TPR) computed using Equation (19), and the other was the false positive rate (FPR) computed using Equation (20). Eventually, the ROC curve was drawn by plotting the FPR and the TPR on the horizontal and vertical axes, respectively.


**Table 3.** Labeling of data according to its predicted label and actual label.

#### *4.5. Flowchart of Conducting the LSM*

In general, the process to conduct the LSM using the proposed TFN-AHP method can be summarized as following 5 steps. Firstly, the 10 LCFs (criteria) that were required to perform the LSM were chosen (as described in Section 3). Then, a two-level hierarchical model was developed with 10 criteria and 41 subcriteria. Next, 11 comparison matrices were established to calculate the criteria weights. After that, using a WLC of weights of all levels, an LSI map was created and reclassified. Finally, the accuracy of the obtained map was validated using ROC curve and the known historical landslides.
