On a value of a matrix game with fuzzy sets of player strategies

Abstract

The present paper investigates a fuzzy matrix game with fuzzy sets of player strategies. We construct a game value with the help of Zadeh's extension principle in combination with an approach to fuzzy matrix games worked out by Liu and Kao. We prove that the FSs of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set (T2FS) on the real line. Furthermore, the corresponding type-2 membership function is given. It is shown that the T2FS of the game value can be decomposed according to the secondary membership grades into a finite collection of fuzzy numbers. Each of them is the value of the corresponding fuzzy matrix game for crisp sets of player strategies. These sets are the corresponding cuts of the original fuzzy sets of player strategies. Illustrative examples are given.