Uncertainty quantification method and application of landslide susceptibility zoning based on fuzzy mathematics

Landslide susceptibility zoning boundary uncertainty is an important issue that affects the reliable interpretation of landslide susceptibility assessment (LSA). To address the downstream uncertainty introduced by the discretization of continuous susceptibility indices, this study proposes an uncertainty quantification framework integrating fuzzy logic and information entropy theory. A case study in Kang County, Gansu Province, China, the results indicate that: (1) the Random Forest (RF) model achieved satisfactory predictive performance (AUC = 0.830), providing a reliable basis for downstream uncertainty quantification; (2) areas with high uncertainty are mainly distributed in the transition zones between different susceptibility levels and in the northeastern part of the county, whereas low uncertainty areas are predominantly distributed in the southern region, with a pronounced clustering pattern in the southwestern; and (3) comparative validation using the Support Vector Machine (SVM) model demonstrates that the spatial patterns of uncertainty are highly consistent across different models, indicating the robustness and applicability of the proposed framework. The results suggest that susceptibility zonation based on classification methods such as Jenks inevitably introduces boundary fuzziness, and the proposed framework can serve as an effective complement to conventional LSA by identifying low reliability areas and providing support for the optimization of susceptibility zonation.