Interactive Decision Making for Multiobjective 0-1 Programming Problems with Fuzzy Parameters through Genetic Algorithms

Abstract

In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective 0-1 programming problems involving fuzzy numbers are formulated. Using the α-level sets of the fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced.Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree α and the reference objective values, corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problem through genetic algorithms with double strings. Then an interactive decision making method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.