Decision making in water resources with fuzzy information

Abstract

The multiple objectives optimization in water resources planning consists in trading multiple and conflicting objectives, forming a complex and dynamic process. In the last four decades multi-objective decisions based on fuzzy sets have been evolved and considerable research spawned into the application of fuzzy subsets. Multiobjective decisions problems with uncertainty require: a) evaluating how well each alternative or choice satisfies each objective and b) combining the objectives into an overall objective or decision function D for the selection of the best alternative. In particular when one has a) a universe of n alternatives X={X1, X2,…Xn} and a set of p objectives (criteria) A={A1,A2,….Ap} to be satisfied, the overall objective is D=A1 and A2 …….and Ap, given by the intersection of all the objectives, D= A1 ∩ A2 …… ∩ Ap and one is seeking solutions satisfying D, with µD(X*)=max(µD(X)), where µD(X) is the grade of membership that the decision function D has for each alternative. An application of the above theory concerns the decision of selecting the most appropriate from five dams and their corresponding reservoirs in Néstos watershed (Alternatives AB, AD, AR, BA, and MA). The criteria set is A= {A1=cost of the dam, A2=environmental impact, A3=Hydroelectric power production, A4=flood protection) and finally the importance set is: P= {b1, b2, b3, b4}.