Water resources management under dual uncertainties: a factorial fuzzy two-stage stochastic programming approach

In this study we propose a factorial fuzzy two-stage stochastic programming (FFTSP) approach to support water resources management under dual uncertainties. The dual uncertainties in terms of fuzziness in modeling parameters and variability of alpha-cut levels are taken into account. As different alpha-cut levels are assigned to each fuzzy parameter (instead of an identical alpha-cut level), the effects of alpha-cut levels on fuzzy parameters can be considered. Factorial analysis method is integrated with fuzzy vertex method to tackle the interactive effects of fuzzy parameters within a two-stage stochastic programming framework. The effects of the interactions among fuzzy parameters under various alpha-cut level combinations can be examined. The FFTSP approach is applied to a water resources management case to demonstrate its applicability. The results show that this approach can not only give various optimized solutions according to decision makers' confidence levels but also provide in-depth analyses for the effects of fuzzy parameters and their interactions on the solutions. In addition, the results show that the effects of diverse alpha-cut combinations should not be disregarded because the results may differ under some specific alpha-cut combinations. The dual sequential factorial analyses embedded in the FFTSP approach guarantee most variations in a system can be analyzed. Therefore water managers are able to gain sufficient knowledge to make robust decisions under uncertainty.