An interactive fuzzy satisficing method for multiobjective 0–1 programming problems with fuzzy numbers through genetic algorithms with double strings

• Published in: European journal of operational research Vol. 107; no. 3; pp. 564 - 574
• Main Authors: Sakawa, Masatoshi, Shibano, Toshihiro
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.06.1998; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Fuzzy goals; Fuzzy logic; Fuzzy numbers; Genetic algorithms; Interactive methods Genetic algorithms; Linear programming; Mathematical programming; Multiobjective 0–1 programming; Operational research and scientific management; Operational research. Management science; Operations research; Pareto optimum; Studies; α-Pareto optimal; Fuzzy goals; α-Pareto optimal; Interactive methods Genetic algorithms; Multiobjective 0–1 programming; Fuzzy numbers; Interactive method; Zero one programming; Pareto optimum; Genetic algorithm; Decision making; Minimax problem; Multiobjective programming; Fuzzy number
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/S0377-2217(97)00197-5

In this paper, by considering the experts' vague 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 a-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision maker (DM) for the objective functions are quantified by eliciting the corresponding linear membership functions. Through the introduction of an extended Pareto optimality concept, if the DM specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the DM 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.