Linguisitc representation of Nash equilibriums in fuzzy games

Fuzzy preference relation has been a useful tool in decision making situations to choose and compare between alternatives. In this paper we show how fuzzy linguistic preference relation can be used in game theory. A fuzzy IF-THEN rule set is constructed to derive preferences according to difference between payoffs. Then using a linguistic choice function, priority of each payoff is derived. We interpret the priorities as the linguistic Nash equilibriums. Also for comparing between fuzzy variables, two measures are introduced including possibility and amount of being greater using fuzzy extension principle.