Effect of averaging operators in fuzzy optimization of reservoir operation

Abstract

Fuzzy multiobjective decision making models generally rely on the aggregation of the objectives to form a decision function. The generalized averaging operator is usually adopted for aggregating multiple and unequal objectives because it allows trade-off amongst the objectives, and has been shown to be suitable to model human decision making behavior. In the field of water resource management, most of the decision-making problems involving the generalized averaging operator implicitly assume the decision maker (DM) is rather optimistic. The analysis of the DM's behavior during the aggregation process and its impact on the performance of the system, has therefore never been addressed by many researchers and decision makers. The aim of this paper is to investigate the relationship between decision makers' index of optimism and the long-term performance of a reservoir resource. More specifically, the generalized averaging operator, whose parameter can be interpreted as the DM's index of optimism, is imbedded into a fuzzy stochastic dynamic program (FSDP). This approach is developed and implemented to derive optimal operating policies for the hydroelectric complex of the Uruguay River basin in Southern Brazil. FSDP-derived policies with different indices of optimism are then compared with simulation. We show that system performance may be influenced by the decision maker's behavior during the aggregation, and that the optimistic assumption may not yield to satisfactory results, especially during critical time periods.