Linguistic Fuzzy-Logic Social Game

Abstract

In Chapter 4, I developed a new game-theoretic approach based, not on conventional Boolean two-valued logic, but instead on linguistic fuzzy logic which admits linguistic truth values. A linguistic fuzzy game is defined with linguistic fuzzy strategies, linguistic fuzzy preferences, and the rules of reasoning and inferences of the game operate according to linguistic fuzzy logic, not Boolean logic. This leads to the introduction of a new notion of fuzzy domination and Nash equilibrium which are based not on the usual ”greater than” relation ordering but rather on a more general form of relation termed linguistic fuzzy relation. Each agent models others as linguistic fuzzy rational agents and tries to find a linguistic fuzzy Nash equilibrium that will achieve the highest linguistic fuzzy payoff.