Decision making in water resources with fuzzy information

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 multiobjective
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}.