Methods of decision making in fuzzy environment and their applications

Results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented. Much attention is given to considering die uncertainty of goals associated with a multicriteria character of many optimization problems. Two classes of models ((X,M) and (X, R) models) are considered with applying the Bellman-Zadeh approach and fuzzy preference relations to their analysis. The consideration of (X, R) models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and analyzing one and the same problem within the framework of interrelated models. It allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with applying one of two techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve problems of power engineering.