Matrix games with linguistic intuitionistic fuzzy Payoffs : Basic results and solution methods

Game theory has found successful applications in different areas to handle competitive situations among different persons or organizations. Several extensions of ordinary game theory have been studied by the researchers to accommodate the uncertainty and vagueness in terms of payoffs and goals. Matrix games with payoffs represented by interval numbers, fuzzy numbers, and intuitionistic fuzzy numbers have considered only the quantitative aspects of the problems. But in many situations, qualitative information plays a crucial role in representing the payoffs of a game problem. This work presents a valuable study on matrix games with payoff represented by linguistic intuitionistic fuzzy numbers (LIFNs). First, the paper defines some new operational-laws for LIFNs based on linguistic scale function (LSF) and studies their properties in detail. Next, we define a new aggregation operator called 'generalized linguistic intuitionistic fuzzy weighted average (GLIFWA)'operator for aggregating LIFNs. Several properties and special cases of GLIFWA operator are also discussed. The LSF provides an ability to consider the different semantic situations in a single formulation during the aggregation process. Further, the paper introduces some basic results of matrix games with payoffs represented by LIFNs. We develop solution methods using a pair of auxiliary linear/nonlinear-programming models derived from a pair of nonlinear bi-objective programming models. Finally, a real-life numerical example is considered to demonstrate the validity and applicability of the developed methods.