Solving matrix games based on Ambika method with hesitant fuzzy information and its application in the counter-terrorism issue

Abstract

The hesitant fuzzy set has been studied as a powerful tool to describe the decision makers’ judgements under uncertain environment and applied to many domains. For solving the matrix games whose payoffs are expressed by the hesitant fuzzy information, the paper proposes the Ambika method of hesitant fuzzy matrix games (HFMGs). In this paper, firstly, the formal representation of HFMGs is established to meet the conditions of two-person finite zero-sum games. Secondly, after a new method of adding elements to the shorter hesitant fuzzy elements (HFEs), i.e. the hesitant fuzzy elements with possibility, is developed to keep the same length of HFEs, a weighting method based on the position of element in the HFEs is proposed. Then the hesitant fuzzy bi-objective nonlinear programming models for both players are established for HFMGs. Thirdly, according to the proposed value and ambiguity indexes, the Ambika method of HFMGs is developed to find the optimal solutions of mixed strategies by solving the converted linear programming models. Finally, as the illustration of the proposed method, a numerical example about how to choose the optimal solutions for a state security department is given in the counter-terrorism issue.