Study on Optimal Allocation of Water Resources Based on Uncertain Multi-Objective Fuzzy Model: A Case of Pingliang City, China

Water shortages are serious in northwest China due to the level of social and economic development, engineering, resource shortages, and other factors being restricted, so the conflict between supply and demand for water resources is prominent in different regions and different water use sectors. Therefore, Pingliang City was selected as the research object in this study. The membership function was introduced, and an interactive algorithm to correct model parameters based on the fairness constraint was derived. An uncertain multi-objective fuzzy programming model was also established. The results show that the optimal allocation of water will be 38,051.9~40,740 × 104 m3 and 39,938.4~41,317.5 × 104 m3 under a normal year (p = 50%) and a dry year (p = 75%) in 2025, respectively, and the corresponding water shortage rates will be 4.2% and 6.7%. In 2035, the optimal water allocation will be 45,644.1~49,245.9 × 104 m3 and 46,442.4~50,044.2 × 104 m3 and the water shortage rates will be 7.0% and 7.0%, respectively. The proportion of groundwater supply will decrease by 8.8% and 13.8% in 2025 and 2035 after the optimal allocation, the proportion of surface water supply will increase by 9.6% and 12.2%, and the proportion of reclaimed water will increase by −0.78% and 2.1%, respectively. The results can provide a technical reference for the development and utilization of water resources in other cities and similar areas in semi-arid regions.