Commentary on “New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making”

Abstract

Liu and Luo (Pattern Anal Appl https://doi.org/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.