## 6 Conclusions  
1. This study successfully developed and applied a fuzzy membership-based method for calculating negative sample credibility for landslide susceptibility assessment. The proposed approach triggers a paradigm shift: from defining \"where to select negative samples\" to quantitatively evaluating \"how reliable the selected samples are.\" The proposed method not only overcomes the significant limitations of conventional sampling methods (such as inadequate spatial continuity and fragmented representations of environmental feature spaces) but also establishes an intuitive and quantifiable reliability metric (i.e., credibility) for negative landslide samples. The resulting credibility distribution map of the negative samples exhibits exceptional spatial continuity and effectively characterizes the nonlandslide spatial patterns, thereby substantially enhancing the scientific rigor and reliability of negative sample selection. Crucially, the proposed method provides robust theoretical and operational support for constructing high-precision landslide susceptibility models;
2. Systematic validation using SVM and RF models confirms that negative samples with credibility thresholds in the 0.7-1.0 range represent the optimal choice for balancing model performance and landslide distribution characteristics. Selecting negative samples within this threshold range enables the generation of scientifically robust landslide susceptibility maps. The results were systematically validated across two distinct ML models, demonstrating the broad applicability of the credibility mapping framework and the proposed sampling methodology. The proposed approach establishes a robust theoretical framework for selecting reliable negative samples in the study area and analogous regions;
3. The primary contribution of this study lies in its pioneering application of fuzzy membership theory to spatialized quantitative representation of negative sample credibility, which provides a novel and effective technical solution to the long-standing challenge of negative sample quality in landslide susceptibility modeling. The generated continuous, high-resolution credibility distribution map deepens our understanding of the spatial heterogeneity in \"nonlandslide areas\" and its latent association with landslide occurrence mechanisms. This result provides a reliable tool for geoscientists to select high-credibility negative samples and provides critical technical support for disaster managers in generating high-fidelity susceptibility maps and robust scientific foundations for land-use planning and disaster risk reduction policy formulation across diverse regions.  
Conceptualization, Y.T. and Z.N.; Methodology, Y.T. and Z.N.; Formal analysis, Z.N.; Investigation, Z.N.; Writing--original draft preparation, Z.N.; Writing--review and editing, Z.N.; Supervision, Y.T.; Funding acquisition, Y.T. All authors have read and agreed to the published version of the manuscript.  
This study was primarily supported by the following research grants: Yunnan Provincial High-Tech Special Project \"Research on the Susceptibility Mechanisms and Risk Prevention of \"Major Geological Disasters in the Wumeng Mountain Area\" (Project No. 202403 AA080001); Activity Prediction and Risk Identification of Large-Scale Plateau Debris Flows\" (Project No. XZ202401 ZY0029); \"Formation Mechanisms and Monitoring-Warning Methods for Morraine Soil Debris Flows in the Eastern Himalayan Syntaxis Region\" (Project No. XZ202401 ZR0073).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available on request from the corresponding author ([EMAIL_ADDRESS]).  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.