Solutions of matrix games involving linguistic interval-valued intuitionistic fuzzy sets

Abstract

Game theory has found significant applications in a wide range of fields to deal with competitive environments between individuals or organizations. The researchers investigated several augmentations of ordinary game theory to deal with uncertainty and ambiguity in payoffs and goals. However, the quantifiable parts of the problems have been studied in matrix games with payoffs expressed by interval numbers, fuzzy numbers, and intuitionistic fuzzy numbers. In several situations, qualitative information is critical in describing the payoffs of a game problem. Experts frequently prefer expressing their perspective in natural linguistic terms rather than numerical values in real-life decision-making challenges. This linguistic representation has been utilized to resolve plenty of decision-making problems. This paper explores the theory of matrix games under a qualitative information environment. We use linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) to describe the payoff values as suggested by experts. The LIVIFNs are more efficient tools that provide experts with a flexible information modeling capability to describe their ambiguous and uncertain perceptions in the form of linguistic terms. The solution of this class of matrix games is attained by resolving a duo of linear or nonlinear programming problems originating through nonlinear bi-objective programming problems. Finally, a numerical example is presented to demonstrate the applicability of the suggested approach.