A novel similarity cloud model for assessing the ecological health of typical rivers in arid northwestern China

Rivers serve as a critical foundation for social and economic sustainable development, particularly in the arid and semi-arid regions of Northwest China. However, intensifying human activities severely threatens the health of rivers. Thus, this study aimed to systematically assess the health status of rivers in these areas. Specifically, the Diannong River and the Kushui River were selected as the study areas. A comprehensive indicator system that integrates ecological integrity (including physical habitat integrity, hydrological integrity, and biological integrity) and non-ecological performance (social service functions) was developed. The weights of the indicators were determined by a game-theoretic approach. A multidimensional similarity cloud model was established for river health assessment. Additionally, a novel similarity calculation method (SBIO) based on the inner and outer products of fuzzy subsets was proposed, demonstrating stronger noise resistance and stability. Comparative analyses with SES, ECM, and SDSL models suggest that the SBIO model provides a uniquely robust and inclusive similarity measurement under varying entropy and hyper-entropy conditions, yielding consistently higher similarity values and the flattest response curve. From the perspectives of both artificial and natural rivers, key issues affecting ecological health in Northwestern China were identified. The results reflect that both the Diannong and Kushui Rivers are in an overall “Unhealthy” state, with approximately 70 % of their indicators rated as “Unhealthy” or worse. Reduced river connectivity, driven by urbanization and water conservancy projects, emerges as the core issue, followed by non-compliance with chemical oxygen demand (CODCr) and total nitrogen (TN) levels. In the Diannong River, TN, CODCr, and permanganate index (CODMn) exceed standard limits by 1.02–1.60 times during non-water supplementation periods. In the Kushui River, TN and CODCr exceed standards by up to 3.93 and 5.14 times annually at most sites. Furthermore, significant alterations appeared in the structure of local aquatic biological communities. This study provides strategies and recommendations for improving river health and promoting sustainable water resource management in Northwest China.