A note on “A novel defuzzification approach of type-۲ fuzzy variable to solving matrix games: An application to plastic ban problem”

Seikh et al. (Iranian Journal of Fuzzy Systems, ۱۸(۵) (۲۰۲۱), ۱۵۵-۱۷۲) pointed out that there does not exist any approach to solve type-۲ fuzzy variable matrix games (matrix games in which each element of the payoff matrix is represented by a type-۲ fuzzy variable). To fill this gap, Seikh et al. proposed an approach to solve triangular type-۲ fuzzy variable (TT۲FV) matrix games (matrix games in which each element of the payoff matrix is represented by a TT۲FV). Seikh et al. also solved a real-life TT۲FV matrix game (plastic ban problem) to show the applicability of their proposed approach. In future, other researchers may use Seikh et al.’s approach to solve other real-life TT۲FV matrix games. However, it is inappropriate to use Seikh et al.’s approach as it may fail to find a correct optimal solution of TT۲FV matrix games. To validate this claim, a TT۲FV matrix game is solved by Seikh et al.’s approach and it is shown that the obtained optimal solution is not correct. Also, it is pointed out that this inappropriateness occurs as a mathematically incorrect result is considered in Seikh et al.’s approach. Furthermore, Seikh et al.’s approach is modified to resolve its inappropriateness.

کلیدواژه ها:

triangular type-۲ fuzzy variable ، matrix games ، plastic ban problem