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Shakeel et al. (Soft Comput 24: 1585–1597, 2020) proposed the concept of a Pythagorean uncertain linguistic hesitant fuzzy set (PULHFS), some arithmetic operations of Pythagorean uncertain linguistic hesitant fuzzy sets (PULHFSs), an approach for comparing PULHFSs and a Pythagorean uncertain linguistic hesitant fuzzy weighted averaging (PULHFWA) operator as well as it extensions. Also, using the proposed comparing approach and the proposed aggregation operators, Shakeel et al. proposed a method for solving multi-attribute group decision making (MAGDM) problems. In future other researchers may use Shakeel et al.'s work in their research work. However, it is observed that the approach for comparing PULHFSs and aggregation operators, proposed by Shakeel et al. (Soft Comput 24: 1585–1597, 2020), are not appropriate. Hence, the method for solving MAGDM problems, proposed by Shakeel et al., is also not appropriate. The aim of this note is to make the researchers aware of the inappropriateness of Shakeel et al. work. Furthermore, point out that to resolve the inappropriateness of Shakeel et al. work (Soft Comput 24: 1585–1597, 2020) is a challenging open research problem. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]