Research on dynamic evaluation and evolution trend of regional water resources carrying capacity based on the coupling of semi-partial subtraction set pair potential and triangular fuzzy numbers

Accurate dynamic assessment of water resource carrying capacity (WRCC) plays a pivotal role in urban sustainability governance. This study developed a comprehensive evaluation framework for regional WRCC, comprising an indicator system with standardized assessment criteria. We proposed an innovative methodology for computing dynamic difference coefficients by integrating semi-partial subtraction set pair potential with triangular fuzzy numbers, subsequently constructing a coupled dynamic evaluation model. Using Hefei City(Anhui Province, China) as a demonstrative case, our analysis reveals:(1) Compared with the level characteristic value method based on set pair analysis, the proposed method reduces the evaluation error of sample evaluation grade values by 1.6 %. Moreover, it is confirmed that the difference coefficient exhibits significant dynamic variation characteristics with both samples and time, which significantly enhances the dynamics, inclusiveness, and rationality of sample evaluation results. (2) From the temporal dimension, the overall WRCC of Hefei is in a state of equi-potential and partial anti-potential. The potential value decreased from −0.148(2012) to −0.196(2023), with an average annual decline rate of 2.95 %, indicating that the WRCC tends to deteriorate.(3) From the spatial distribution perspective, the WRCC of the Shixiaqu is the worst (moderate overload status), followed by Changfeng County, Feixi County, Feidong County, and Lujiang County (slight overloaded status), and then Chaohu City (critical status).This systematic approach provides multidimensional insights into Hefei's WRCC evolution, establishing a scientific foundation for adaptive water resource management strategies and water security enhancement in rapidly urbanizing regions.