Linguistic Fuzzy-Logic Game Theory

The author develops a new game-theoretic approach, anchored not in Boolean two-valued logic but instead in linguistic fuzzy logic. The latter is characterized by two key features. First, the truth values of logical propositions span a set of linguistic terms such as true, very true, almost false, very false, and false. Second, the logic allows logical categories to overlap in contrast to Boolean logic, where the two possible logical categories, “true†and “false,†are sharply distinct. A game becomes a linguistic fuzzy logic game by turning strategies into linguistic fuzzy strategies, players’ preferences into linguistic fuzzy preferences, and the rules of reasoning and inferences of the game into linguistic fuzzy reasoning operating according to linguistic fuzzy logic. This leads to the introduction of a new notion of linguistic fuzzy domination and linguistic Nash equilibrium.