Approaches to Solve Matrix Games and Bi-Matrix Games Under Different Fuzzy Environments

Abstract

In this thesis, it is pointed out that some mathematically incorrect results are considered in (i) Seikh and Dutta (2022)’s approach to solve SVTrN MGs. So, Seikh and Dutta (2022)’s approach is not valid. Also, a valid approach is proposed to solve SVTrN MGs. (ii) The existing methods (Qiu and Xiang, 2022; Chauhan and Gupta, 2023) to solve 2TL BMGs. So, the existing methods (Qiu and Xiang, 2022; Chauhan and Gupta, 2023) are not valid. Also, a valid method is proposed to solve 2TL BMGs. (iii) An and Li (2019)’s approach to solve constrained IF BMGs. So, An and Li (2019)’s approach is not valid. Also, a valid approach is proposed to solve constrained IF BMGs. (iv) Mi et al. (2021)’s method to solve PL MGs. So, Mi et al. (2021)’s method is not valid. Also, a valid method is proposed to solve PL MGs. (v) Singh et al. (2020)’s approach to solve two-player constant-sum 2TL MGs. (vi) Seikh et al. (2021)’s approach to solve TT2FV MGs. So, Seikh et al. (2021)’s approach is not valid. Also, a valid approach is proposed to solve TT2FV MGs. (vii) Karmakar et al. (2021)’s method to solve type-2 IF MGs. So, it is inappropriate to use Karmakar et al. (2021)’s method. Also, the required modifications are suggested to resolve the inappropriateness of Karmakar et al. (2021)’s method.