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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]

Qiyas et al. (Int J Fuzzy Syst, 22: 310–320, 2020) proposed a linguistic picture fuzzy number (LPFN), an approach for comparing linguistic picture fuzzy numbers (LPFNs), some operational laws on LPFNs and a linguistic picture fuzzy weighted averaging (LPFWA) operator. In this commentary, some flaws that exist in Qiyas et al.'s approach for comparing LPFNs, Qiyas et al.'s operational laws and Qiyas et al.'s LPFWA operator have been pointed out. [ABSTRACT FROM AUTHOR]

Liu and Luo (Pattern Anal Appl 10.1007/s10044-017-0635-6) proposed a single-valued neutrosophic hesitant fuzzy ordered weighted aggregation (SVNHFOWA) operator and used it for solving single-valued neutrosophic hesitant fuzzy multi-attribute decision making (MADM) problems. It is pertinent to mention that to show the validity of SVNHFOWA operator, Liu and Luo claimed that this operator satisfies the idempotency, commutativity and monotonicity properties. However, after a deep study, it is observed that the monotonicity property is not satisfying for the SVNHFOWA operator whereas, for the validity of an aggregation operator the monotonicity property should necessarily be satisfied. Therefore, the SVNHFOWA operator, proposed by Liu and Luo, is not valid. Since, in future, the other researchers may use this SVNHFOWA operator in their research work as well as for solving real-life single-valued neutrosophic hesitant fuzzy MADM problems. Therefore, the aim of this paper is to make the researchers aware about the fact that it is scientifically incorrect to use the SVNHFOWA operator. [ABSTRACT FROM AUTHOR]