A note on “A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application”

Abstract

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. A note on "A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application"

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

“…As a result, the term variable is employed in a broader scientific context than in a strictly mathematical context. As shown in the prolongation, the mathematical structure of fuzzy set theory generates a suitable concept of possibility, giving a characteristic similar to that of measure theory regarding probability theory.An ambiguous restriction is an allocation of possibilities, with its membership function serving as a distribution function of possibilities, and a fuzzy attribute is affiliated with an allocation of possibilities in the same way that a probability distribution is attributed with a random variable suggested by Zadeh in this outlook [13]. Assume that the tumor cell population n 0 is described in the sense of tumor population dynamics by a fuzzy set n 01 with membership functionµ n 01 (N ).As a result, for any precise value N = z 0 , the value µ n 01 (z 0 )represents the rate of probability that the dynamical system'sactual initial state of tumor takes the value z 0 given that the initial cell count of the tumor is precisely n 0 .…”