Fuzzy preference relations in models of decision making

Analysis of < X, R > models is considered as part of a general approach to solving optimization problems with fuzzy coefficients. This approach involves a modification of traditional optimization methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models by constructing equivalent analogs with fuzzy coefficients in objective functions alone. The use of the approach allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is based on reducing the problem to multiobjective choice of alternatives in a fuzzy environment. Three techniques for processing of fuzzy preference relations reflecting criteria of quantitative as well as qualitative character are discussed. The results of the paper are universally applicable and are already being used to solve power engineering problems. (C) 2005 Elsevier Ltd. All rights reserved.