Solving hesitant fuzzy linguistic matrix game with regret theory

It is convenient and effective for the two players playing a finite game to describe their utility values using qualitative linguistic information rather than quantifying them with numbers. The hesitant fuzzy linguistic term set (HFLTS) is a handy tool in providing a mathematical representation to the players to define the utility or payoff values of the game. The HFLTS imparts flexibility in expressing uncertainties in complex situations. In this paper, we studied two-person matrix games where the payoffs are HFLTS. Applying the equivalence of linguistic terms to trapezoidal fuzzy numbers, the payoffs are converted into fuzzy intervals with the two end-points as trapezoidal fuzzy numbers. Using the subjective sensation scale, the payoffs are converted to crisp intervals. We design a methodology to determine the Nash equilibrium of the game under the regret theory setup that helps the players to reduce the possibility of regret perception in their optimal choice of mixed strategies. We illustrate the procedure with an example. We also performed a sensitivity analysis of solutions of games concerning certain parameters involved in our designed methodology. A brief comparison is included comparing recent works in a similar direction.