Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Abstract

Seikh and Dutta (Soft Computing (2022) 26:921–936) pointed out that there does not exist any approach to solve single-valued trapezoidal neutrosophic (SVTN) matrix games (matrix games in which each payoff is represented by a SVTN number). To fill this gap, Seikh and Dutta proposed two approaches to solve SVTN matrix games. Brikaa (Soft Computing (2022) 26:9137–9139) pointed out that it is inappropriate to use Seikh and Dutta’s first approach as a mathematically incorrect result is considered in it. Brikaa also modified Seikh and Dutta’s first approach to resolve its inappropriateness. In this paper, it is pointed out that it is also inappropriate to use Brikaa’s approach as some mathematically incorrect results are considered in it. Also, it is pointed out that it is inappropriate to use Seikh and Dutta’s second approach as a mathematically incorrect result is considered in it. Furthermore, Brikaa’s approach and Seikh and Dutta’s second approach are modified to resolve their inappropriateness. Finally, the correct results of a SVTN matrix game, considered by Seikh and Dutta to illustrate their proposed approaches, are obtained by the modified approaches.