Vertex method for computing functions of fuzzy variables
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Development of an optimization model for water resources systemsplanning
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In this study, a multistage fuzzy-stochastic programming (MFSP) model is developed for tackling uncertainties presented as fuzzy sets and probability distributions. A vertex analysis approach is proposed for solving multiple fuzzy sets in the MFSP model. Solutions under a set of @a-cut levels can be generated by solving a series of deterministic submodels. The developed method is applied to the planning of a case study for water-resources management. Dynamics and uncertainties of water availability (and thus water allocation and shortage) could be taken into account through generation of a set of representative scenarios within a multistage context. Moreover, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The modeling results can help to generate a range of alternatives under various system conditions, and thus help decision makers to identify desired water-resources management policies under uncertainty.