A note on “Dealer using a new trapezoidal cubic hesitant fuzzy TOPSIS method and application to group decision-making program”

Abstract

Amin et al. (Soft Comput 23:5353–5366, 2019), firstly, proposed a trapezoidal cubic hesitant fuzzy weighted geometric (TrCHFWG) aggregation operator for aggregating trapezoidal cubic hesitant fuzzy sets (TrCHFSs). Then, using the proposed aggregation operator, Amin et al. proposed TOPSIS (Technique for order preference by similarity to ideal solution) method for solving multi-attribute group decision making problems under TrCHFS environment. In this note, it is pointed out that Amin et al.’s aggregation operator is not valid as the monotonicity property is not satisfied for Amin et al.’s TrCHFWG aggregation operator. Hence, it is inappropriate to use Amin et al.’s TOPSIS method. Also, it is pointed out that to resolve the inappropriateness of Amin et al.’s TrCHFWG aggregation operator as well as Amin et al.’s TOPSIS method is an open challenging research problem.