Fuzzy preference relations methods and power engineering applications

Two classes of problems are considered within the framework of a general approach to solve optimisation problems with fuzzy coefficients, referred to as <X,M> and <X,R> models in the literature. This paper is concerned with the latter and proposes an approach which replaces the initial problem by a set of associated mutually interrelated models. To reduce the decision uncertainty region, the problem is converted to a multicriteria decision problem in a fuzzy environment using two methods. The first method reduces the region sequentially through a step-by-step comparison of alternatives. The second method analyses membership functions of a subset of non-dominated alternatives, considering all criteria simultaneously. The results have general applicability and are being used in power engineering planning in Brazil.