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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]

Garg and Arora (2018) pointed out that it is not appropriate to use the existing intuitionistic fuzzy soft (IFS) aggregations operators (Arora and Garg, 2018a,b), proposed by themselves, as these aggregation operators gives undesirable results under some circumstances. To resolve the flaws of these aggregation operators, Garg and Arora (2018) proposed the improved operational laws of IFS numbers and hence, proposed a new IFS aggregation operator (named as Scaled prioritized intuitionistic fuzzy soft interaction (SPIFSI) aggregation operator). Garg and Arora (2018) also proposed a SPIFSI aggregation operator based intuitionistic fuzzy soft multi criteria decision making (IFSMCDM) approach for solving IFSMCDM problems (Multi criteria decision making problems in which the rating value of each alternative over each criterion is represented by an IFS set). Although, Garg and Arora (2018) have claimed that their proposed SPIFSI aggregation operator is valid as it satisfies the idempotency, boundedness and monotonicity properties. But, in actual case, for the SPIFSI aggregation operator, proposed by Garg and Kumar (2018), the monotonicity property is not satisfying. Therefore, the SPIFSI aggregation operator, proposed by Garg and Arora (2018), and hence, the SPIFSI aggregation operator based IFSMCDM approach, are not valid. Since, in future, other researchers may use the SPIFSI aggregation operator in their research work. Also, the researchers may use the SPIFSI aggregation operator based IFSMCDM approach for solving real life IFSMCDM problems. Therefore, the aim of this note is to make the researchers aware about the discrepancies of the SPIFSI aggregation operator as well as the SPIFSI aggregation operator based IFMCDM approach. Furthermore, to make the researchers aware that improved operational laws of IFS numbers, proposed by Garg and Arora (2018), are also not valid. [ABSTRACT FROM AUTHOR]