在充分考虑水资源系统中供需水不确定性的基础上，基于多目标规划、模糊规划和区间规划原理，以经济效 益、社会效益和环境效益最大为目标，以需水量、可供水量和不同子区用水部门间的用水公平性为主要约束，构 建一种适用于多水源、多子区、多用户的考虑供需水不确定性的多目标模糊规划模型，以期通过平衡水资源配置 系统中用户配置水量、缺水风险与系统收益三者的关系，实现系统综合效益最大。模型以衡水市历年供水、用水 及社会经济等数据确定规划年的水资源参数及经济参数，采用区间参数反映系统中的不确定性，通过引入模糊隶 属度函数，利用两步交互式算法，将多目标规划转化为单目标规划进行求解，以 2025 年为衡水市规划水平年，得 到规划水平年下的 11 个子区、4 种水源、4 个用水行业的最优配水方案。结果表明：本研究制定的水资源优化配 置方案可实现“外调水优先利用、地下水控制利用”，同时考虑用水的公平性约束后，在缺水条件下可有效控制水 资源向每立方米水效益高的区域和部门流动，有利于多区域、多部门共担缺水风险；该水资源优化配置方案可有 效缓解衡水市水资源供需矛盾，实现多水源和多目标之间的协同互补。研究成果可为河北省其他县域的水资源 优化配置提供技术参考。

Based on the principles of multi-objective planning, fuzzy planning and interval planning, with the goal of maximizing economic, social and environmental benefits, and taking water demand, water availability and water fairness between water departments in different sub-districts as the main constraints, a multi-objective fuzzy planning model based on uncertainty suitable for multiple water sources, multiple sub-areas and multiple users is constructed, and strives to balance the amount of user-allocated water in the water resources allocation system. The relationship between water shortage risk and system benefits maximizes the comprehensive benefits of the system. The model transforms the multi-objective program into a single-objective program by introducing a fuzzy membership function and using a two-step interactive algorithm. The model is also applied to the optimal allocation of water resources in Hengshui City, Hebei Province, and an optimal water allocation plan for 11 sub-areas, four water sources and four water consuming industries is obtained for the planning level in 2020. The results indicate that the method can be used to study the optimal allocation of water resources between multi-source, multi-area, and multi-water sectors. The optimal model achieves complementarity between multiple water sources and multiple objectives, and provides a decision-making basis for optimal allocation of water resources in arid and water-deficient areas. At the same time, after considering the fairness constraint of water use, under the condition of water shortage, the flow of water resources to regions and sectors with high unilateral water efficiency can be effectively controlled, which is conducive to multi-regional and multi-sectoral sharing of water shortage risks. The research results can provide technical reference for the optimal allocation of water resources in other counties in Hebei Province.