A note on “Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making”

Abstract

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.