A general approach to solving a wide class of fuzzy optimization problems

Results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented. A general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described. It involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms. Prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone. The results of the paper are of a universal character and are already being used to solve problems of power engineering. (C) 1998 Elsevier Science B.V. All rights reserved.