Coupling Coordination Degree Evaluation of Regional Water Resources, Social Economy and Ecological Environment Composite System Based on Logical Multiplication of Connection Numbers and Stochastic Simulations.

Traditional coupling coordination degree (CCD) evaluation methods fail to simultaneously ensure the accuracy and reliability of evaluation results. To overcome this limitation, a novel evaluation method that integrates the logical multiplication of connection numbers with stochastic simulations (ECCD-LMS) is developed to assess the CCD of regional water resources, social economy, and ecological environment (WSE) composite systems. The method adopts three-element connection numbers to quantify the comprehensive evaluation level of each system. Overall partial connection numbers and triangular fuzzy numbers then define dynamic value intervals for the connection number components, and the Monte Carlo method is integrated to simulate stochastic variation in each component. The simulated values are substituted into the logical multiplication of connection numbers to generate evaluation results that include both mean CCD estimates and 95% uncertainty intervals. The empirical application of ECCD-LMS in China's Jing River Basin indicated that the coupling coordination level of the regional WSE composite system exhibited an overall increasing tendency with fluctuations from 2012 to 2023. These fluctuations were closely associated with variations in the comprehensive evaluation level of the water resources system. Spatially, the disparities in evaluation grades among subregions gradually narrowed during the study period. Compared with traditional CCD evaluation methods, ECCD-LMS effectively corrects systematic overestimation while maintaining objectivity and produces more dispersed CCD estimates that reflect differences among evaluation samples with greater clarity. Furthermore, by outputting mean CCD estimates and 95% uncertainty intervals, ECCD-LMS outperforms traditional methods that only provide static point estimates. It thus enables robust and credible evaluation of the coupling coordination level of WSE composite systems under multiple sources of uncertainty, suggesting potential applicability across diverse regional contexts.