A multi-stage fuzzy stochastic programming method for water resources management with the consideration of ecological water demand

In this paper, a multi-stage fuzzy stochastic programming (MFSP) method is introduced to deal with uncertainties presented as fuzzy sets and probability distributions. Moreover, it is able to reflect dynamics of uncertainties and the related decision processes through constructing a series of representative scenarios within a multi-stage context under a set of fuzzy a-cut levels. A management problem about long-term planning of water resources system has been studied to illustrate applicability of the proposed approach. With ecological water demand being considered, the framework solves the complex problems that can hardly be solved in previous individual model research and promotes sustainable development. The results indicate that the dynamic and complexity of water resources allocation can be reflected through the multilayer discrete context tree. Moreover, real-time correction for reducing the risk of water shortage and low economic penalty can be presented. They can also help identify satisfaction degree of the goal and feasibility degree of constraints in an interactive way, enabling decision makers to generate a series of alternatives under various system conditions. Overall, it can not only contribute to decision makers for in-depth analysis, but also for sustainable development of ecosystem.