## 2 Theoretical Framework and Methods
### Uncertainty Measurement Principle  
To accurately grasp the specific conditions of things within a system, it is necessary to quantify uncertainty and calculate numerical values for in-depth analysis. [PERSON] introduced the concept of a fuzzy membership function in his paper \"Fuzzy Sets\", describing the \"phenomenon of vague boundaries\" [26]. This concept expanded research from deterministic sets to uncertain sets, and, on this basis, the emerging discipline of fuzzy mathematics was established. Polish scholar [PERSON], in his paper \"Rough sets\", based on the study of \"indiscernible relations\", constructed the theory of rough sets to describe uncertain information [27]. Furthermore, Professor [PERSON] and his research team conducted an analysis of the distinctions between fuzzy sets and rough sets, leading to the  
Figure 1: Resilience framework for flooding at subway stations. proposal of the concept of uncertainty sets, operational rules, and methods for constructing uncertainty functions. The uncertainty measurement theory is predicated on the premise that decision-makers assess the uncertainty inherent in phenomena within uncertain states and translate this level of understanding into a quantitative ratio. Uncertainty measure theory, as an effective method for dealing with uncertain information, can fully utilize the inherent information value carried by data. It not only eliminates the subjective bias in the decision-making process but also avoids the limitations of other mathematical methods. Therefore, it has been widely applied in evaluation studies across various fields. In the field of urban real estate investment risk assessment, the theory has pioneered a new evaluation model [28]. Furthermore, the combination of uncertainty measure and entropy weight method has provided a more precise perspective for urban rail construction risk assessment [29]. In the field of tunnel gas risk assessment, the combination of uncertainty measure theory and entropy-weight-analytic hierarchy process has formed a more accurate evaluation method [30]. In rockburst risk assessment, uncertainty measure theory, by quantifying uncertain information and combining it with the analytic hierarchy process, has offered a novel evaluation approach [31]. In the subway engineering field, uncertainty measure theory has been introduced to establish a surrounding rock quality evaluation model, and its feasibility and effectiveness have been verified through comparative analysis with cloud models [32]. The stability analysis of foundation pit slopes has also been deeply studied using uncertainty measure evaluation methods [33]. The risk assessment method for high-temperature operations in underground mines has also been constructed through uncertainty measure theory [34]. Additionally, by combining uncertainty measure theory with dynamic, comprehensive weighting methods of fuzzy analytic hierarchy process-entropy weight method and set pair analysis theory, an improved UM-SPA coupling model has been proposed for landslide susceptibility assessment [35]. In the comprehensive evaluation of construction project safety risks, the analytic hierarchy process and information entropy are used to determine weights, and then uncertainty measure theory is applied for evaluation [36]. The normal cloud model optimizes the uncertainty measure theory to enhance the accuracy of rockburst prediction [37]. Set pair analysis theory has also been used to optimize the attribute recognition standards in uncertainty measure theory, and based on this, an optimized comprehensive prediction model for tunnel rockburst trends has been constructed [38]. These studies demonstrate the wide application and effectiveness of uncertainty measure theory in the field of risk assessment. Subway stations are located in complex urban systems where there are many uncertain factors affecting flood disaster resilience, and controllable and uncontrollable factors are intertwined.