Modeling uncertainty in reservoir loss functions using fuzzy sets

Imprecision involved in the definition of reservoir loss functions is addressed using fuzzy set theory concepts. A reservoir operation problem is solved using the concepts of fuzzy mathematical programming. Membership functions from fuzzy set theory are used to represent the decision maker's preferences in the definition of shape of loss curves. These functions are assumed to be known and are used to model the uncertainties. Linear and nonlinear optimization models are developed under fuzzy environment. A new approach is presented that involves development of compromise reservoir operating policies based on the rules from the traditional optimization models and their fuzzy equivalents while considering the preferences of the decision maker. The imprecision associated with the definition of penalty and storage zones and uncertainty in the penalty coefficients are the main issues addressed through this study. The models developed are applied to the Green Reservoir, Kentucky. Simulations are performed to evaluate the operating rules generated by the models considering the uncertainties in the loss functions. Results indicate that the reservoir operating policies are sensitive to change in the shapes of loss functions.