Correlation between intuitionistic fuzzy sets: Some conceptual and numerical extensions

This paper is a continuation and extension of our previous works on a correlation coefficient of Atanassov's intuitionistic fuzzy sets (A-IFSs). The correlation coefficient, an extension of Pearson's r which is one of the most frequently used tools in statistics, we have proposed provides the strength of the relationship between the A-IFSs and also shows if the considered sets are positively or negatively correlated. Moreover, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin. This concept is further dealt with. Moreover, what has not been done so far in the literature, an extended numerical analysis on the well known benchmarks of Pima and Iris data is provided.