Fuzzy linear programming models to solve fuzzy matrix games. (English) Zbl 0675.90098

Campos, L.

Fuzzy Sets Syst. 32, No. 3, 275-289 (1989).

Summary: A zero-sum two-person game with imprecise values in its matrix of payoffs is considered. We propose a method for its solution based on the establishment of a fuzzy linear programming (FLP) problem for each player. The method is shown as a generalization of that conventionally used in the solution of a classical game. To solve such FLP problems we propose the auxiliary models resulting from the application of some of the methods for ranking fuzzy numbers. Hence, according to the kind of of ranking method that players want to use, different solutions to the former game can be obtained. We show that these solutions are of the same nature as the parameters defining the game, and corresponding to a fuzzy predicate that can be established as: “ the value of the game is around v”.

MSC:

91A05	2-person games
90C05	Linear programming
03E72	Theory of fuzzy sets, etc.

Keywords:

fuzzy matrix games; ranking fuzzy numbers

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