Equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals |
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| Authors: | I. Nishizaki M. Sakawa |
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| Affiliation: | (1) Faculty of Business Administration and Informatics, Setsunan University, Ikeda-Nakamachi, Neyagawa, Osaka, Japan;(2) Department of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, Kagamiyama, Higashi-Hiroshima, Japan |
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| Abstract: | Equilibrium solutions in terms of the degree of attainment of a fuzzy goal for games in fuzzy and multiobjective environments are examined. We introduce a fuzzy goal for a payoff in order to incorporate ambiguity of human judgments and assume that a player tries to maximize his degree of attainment of the fuzzy goal. A fuzzy goal for a payoff and the equilibrium solution with respect to the degree of attainment of a fuzzy goal are defined. Two basic methods, one by weighting coefficients and the other by a minimum component, are employed to aggregate multiple fuzzy goals. When the membership functions are linear, computational methods for the equilibrium solutions are developed. It is shown that the equilibrium solutions are equal to the optimal solutions of mathematical programming problems in both cases. The relations between the equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals and the Pareto-optimal equilibrium solutions are considered. |
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| Keywords: | Bimatrix games multiple payoff matrices equilibrium solutions Pareto optimality mathematical programming problems |
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