$$(\alpha , \beta , \gamma )$$-cut set based ranking approach to solving bi-matrix games in neutrosophic environment

Abstract

Uncertainty provides an importance in decision making problems like game theory. Several types of uncertainties occur in the literature as fuzzy, soft, rough, interval, etc., and game theory is treated by these types of uncertainties and vagueness by game theorists and others in different aspects. Neutrosophic set and logic are emerged nowadays as another type of uncertainty. Single-valued triangular neutrosophic numbers liberally assume the indeterminacy in choice of elements based upon decision makers’ intuition, assumption, judgement, behaviour, evaluation and decision. Here, a new ranking approach is based on the $$(\alpha , \beta , \gamma )$$ -cut of single-valued triangular neutrosophic number and is applied on bi-matrix game theory. We compare our derived results with some previously defined score and accuracy functions and put some interesting and comparatively good results without any plausible fiasco. In this paper, our principal purpose is to validate and approve the proposed contemplations by applying it on illuminating real-life problems in neutrosophic realm through bi-matrix game theory.