An interactive fuzzy satisficing method for large scale multiobjective 0-1 programming problems with fuzzy parameters through genetic algorithms

摘要

In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective block angular 0-1 programming problems involving fuzzy numbers are formulated. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-multiobjective 0-1 programming problem is introduced and an extended Pareto optimality concept is defined. For the α-multiobjective 0-1 programming problem, the fuzzy goal of the decision maker for each objective function quantified by eliciting the corresponding membership function is considered. Since the decision maker must select a compromise or satisficing solution from the extended Pareto optimal solution set including an infinite number of elements in general, an interactive fuzzy satisficing method through genetic algorithms for deriving a satisficing solution for the decision maker from an extended Pareto optimal solution set is presented. Then, for fixed α and reference membership levels the corresponding extended Pareto optimal solution can be obtained by solving a minimax problem with block angular structure. In order to solve the minimax problem efficiently, we adopt a genetic algorithm with decomposition procedures. Finally, both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments.