Inexact Fuzzy-Stochastic Programming for Water Resources Management Under Multiple Uncertainties

In this study, an interval-parameter fuzzy-stochastic two-stage programming (IFSTP) approach is developed for irrigation planning within an agriculture system under multiple uncertainties. A concept of the distribution with fuzzy-interval probability (DFIP) is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets, and probability distributions. IFSTP integrates the interval programming, two-stage stochastic programming, and fuzzy-stochastic programming within a general optimization framework. IFSTP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. IFSTP is applied to an irrigation planning in a water resources management system. Solutions from IFSTP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions are generated for objective function values and decision variables; thus, a number of decision alternatives can be generated under different levels of stream flows.