To facilitate regional water resources allocation, an integrated bi-level multi-objective programming (IBMP) model with dual random fuzzy variables was developed in this research The proposed model was derived through incorporating dual random fuzzy variables, multi-objective programming, and interval parameter programming within a bi-level optimization framework. This approach improved upon the previous bi-level programming methods and had two advantages. Firstly, it was capable of reflecting tradeoffs among multiple conflict preferences for water related bi-level hierarchical decision-making processes. Secondly, random fuzzy variables were used to tackle the dual uncertainties in both sides of the constraints, which were characterize as probability density functions and discrete intervals. Then, a real-world water resources planning problem was employed for illustrating feasibility of the application of IBMP model in Dongjiang river watershed of south China. Results reflected the alternative decisions for water allocation schemes under a set of probability levels and fuzzy α - cut levels, which can support in-depth analysis of tradeoffs among multiple levels and objective values. Moreover, modeling comparison analysis was undertaken to illustrate the performances of the proposed model.

为促进区域水资源配置，本研究开发了具有对偶随机模糊变量的集成双层多目标规划（IBMP）模型。该模型是通过结合对偶随机模糊变量、多目标规划和区间参数推导出来的在双层优化框架内进行编程。这种方法改进了以前的双层编程方法，并具有两个优点。首先，它能够反映与水相关的双层分层决策过程的多种冲突偏好之间的权衡。其次，利用随机模糊变量来解决约束两边的双重不确定性，将其表征为概率密度函数和离散区间。然后，通过一个现实世界的水资源规划问题来说明IBMP模型在华南东江流域应用的可行性。结果反映了在一组概率水平和模糊α-割水平下的水资源分配方案的替代决策，可以支持深入分析多个水平和目标值之间的权衡。此外，还进行了建模比较分析，以说明所提出模型的性能。