Discrete optimization algorithms and problems of decision making in a fuzzy environment

Abstract

An approach to solving optimization problems with fuzzy coefficients is described. It consists in formulating and analyzing one and the same problem within the framework of mutually related models by constructing equivalent analogs with fuzzy coefficients in objective functions alone. Since the approach is applied within the context of fuzzy discrete optimization problems, modified algorithms of discrete optimization are discussed. These algorithms are based on a combination of formal and heuristic procedures and allow one to obtain quasi-optimal solutions after a small number of steps, thus overcoming the computational complexity posed by the NP-completeness of discrete optimization problems. The subsequent contraction of the decision uncertainty regions is associated with reduction of the problem to multiobjective decision making in a fuzzy environment using techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve practical problems in several fields.