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An extended fuzzy parametric programming (EFPP) model was proposed for supporting water resources allocation problems under uncertainty. EFPP deals with flexible constraints (i.e., fuzzy relationships) by allowing violation of constraints at certain satisfaction degrees (i.e., α levels) and employs fuzzy ranking method to handle trapezoidal-shaped fuzzy coefficients. The objective function is defuzzified by using β cuts and weighting factors. The applicability of EFPP was demonstrated by a numerical example and a water resources allocation case. A series of decision alternatives at various satisfaction degrees were obtained. Generally, the higher the α level, the lower the system benefit. In comparison, the β level in the objective function posed less sensitive impacts on both objective function and model solutions. The reliability of EFPP was tested by comparing its solutions with those from fuzzy chance constrained programming (FCCP). The results indicated that EFPP performed equally well with FCCP in addressing parameter uncertainties, but it demonstrated a wider applicability due to its extended capacity of handling fuzzy relationships in the model constraints.

Applying an Extended Fuzzy Parametric Approach to the Problem of Water Allocations