Debris flow susceptibility assessment based on Choquet fuzzy integral with small sample size: A case study of Shimian County, Ya’an City

Debris flow susceptibility assessment (DFSA) is frequently hampered by identification bias arising from limited sample sizes, class imbalances, and unreliable negative samples. However, research on optimizing negative samples at the watershed-unit scale remains scarce, and existing methods inadequately capture and quantify the complex nonlinear interactions among influencing factors. To address these limitations, this study proposes a negative sample optimization strategy based on the Choquet fuzzy integral (CFI), designed to screen negative samples with higher informational completeness by quantifying factor interactions. The Shimian County of Ya'an City, Sichuan Province, was selected as the study area, which was delineated into 287 watershed units. Sixteen influencing factors, including slope, rainfall, and lithology, were selected, and 108 watersheds with historical debris flow records were identified. On this basis, a CFI-based sampling strategy was developed and compared against three conventional methods: random sampling, Information Content (IC), and Weights of Evidence (WOE). Susceptibility mapping was subsequently conducted using Random Forest (RF), Support Vector Machine (SVM), and Logistic Regression (LR) on the constructed sample sets. Results indicate that under conventional sampling strategies, AUC values ranged from 0.812 to 0.908 for RF, 0.769 to 0.906 for SVM, and 0.739 to 0.866 for LR, reflecting limited discriminative capability. In contrast, the CFI-based optimization strategy significantly enhanced model performance, achieving AUC values of 0.930, 0.929, and 0.923 for CFI-RF, CFI-SVM, and CFI-LR, respectively, alongside marked improvements in sensitivity and accuracy. The study demonstrates that CFI not only effectively characterizes the nonlinear interaction mechanisms among multiple factors but also enables the quantitative selection of high-quality negative samples, providing a scalable technical framework for debris flow susceptibility mapping (DFSM) under small-sample conditions.