This work aims to study and observe all the existing score functions that help to rank the single-valued neutrosophic set (SVNS) as well as interval-valued neutrosophic set (IVNS) to make a better choice among all the available alternatives in multi-criteria decision-making (MCDM) problems. An intensive study about all these existing score functions reveals that there holds some limitations in the method of ranking order which is misleading the results in decision-making problems. These observations about the existing score functions of the SVNS and IVNS have been claimed with the help of well-defined examples, illustrating an inefficiency of all these existing score functions. Thus, to propose a valid score function for ranking SVNS and IVNS for making a better selection among all the other available alternatives in MCDM problems is still an open challenging research problem.
Garg and Kumar (Scientia Iranica, 2017, https://doi.org/ 10.24200/SCI.2017.4454) proposed some new correlation coefficient between intuitionistic fuzzy sets (IFSs). To point out the advantages of their proposed correlation coefficient over the existing correlation coefficient, Garg and Kumar applied their proposed correlation coefficient as well as the existing correlation coefficient to identify a suitable classifier for an unknown pattern, represented by an intuitionistic fuzzy set (IFS), from the known patterns, each represented by IFS. Garg and Kumar suggested that the existing correlation coefficient fails to identify a suitable classifier, whereas, the correlation coefficient, proposed by them, does not fail to identify a suitable classifier. So, it is appropriate to use the correlation coefficient, proposed by them, instead of the existing correlation coefficient. In this note, it is shown that the correlation coefficient, proposed by Garg and Kumar, also fails to identify a suitable classifier. Furthermore, it is shown that more computational efforts are required to apply the correlation coefficient, proposed by Garg and Kumar, as compared to the existing correlation coefficient. In the actual case, it is inappropriate to apply the correlation coefficient for identifying a suitable classifier.
Ye (Appl. Math. Model. 38 (2014) 659-666) proposed an expression for evaluating the weighted correlation coefficient between two dual hesitant fuzzy sets (DHFSs). Ye claimed that their proposed expression can be used for finding the solution for several real-life multi-attribute decision making (MADM) problems under dual hesitant fuzzy set (DHFS) environment. To validate the claim, Ye solved one real-life problem (finding the best investment company). In future, other researchers may use Ye’s expression for solving same type of real-life problems or some other type of real-life problems. However, after a deep study, it is observed that Ye has used some mathematical incorrect assumptions to obtain his proposed expression i.e., Ye’s expression is not valid in its present form. Therefore, if one will apply this expression then the obtained results may or may not be exact. Keeping the same in mind, Ye’s expression has been modified. Furthermore, using the modified expression, the exact result of the real-life problem, considered by Ye, has been obtained.