Interactive Two-Stage Stochastic fuzzy Rough Programming for Water Resources Management

This paper deals with a fuzzy programming approach for treating an interactive two-stage stochastic rough-interval water resource management. The approach has been developed by incorporating an interactive fuzzy resolution method within a rough two-stage stochastic programming framework. The approach can not only tackle dual rough intervals presented as an inexact boundary intervals that exist in the objective function and the left- and right-hand sides of the constraints that are associated with different levels of economic penalties when the promised policy targets are violated. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers to conduct in depth analysis of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints. A management example in terms of rough-intervals water resources allocation has been treated for the sake of applicability of the proposed approach.