TITLE:
Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games
AUTHORS:
Hitoshi Yano, Ichiro Nishizaki
KEYWORDS:
Multiobjective Two-Person Zero-Sum Games, LR Fuzzy Numbers, Fuzzy Payoff Matrices, Fuzzy Goals, Possibility Measure, Pareto Optimal Solutions, Linear Programming
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.5,
March
18,
2016
ABSTRACT: In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.