A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making

The objective of this work is to present novel correlation coefficient measures for measuring the relationship between the two complex intuitionistic fuzzy sets (CIFSs). In the existing studies of fuzzy and its extension, the uncertainties present in the data are handled with the help of degrees of membership which are the subset of real numbers, and may lose some useful information and hence consequently affect on the decision results. An alternative to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two-dimensional information in a single set. Thus, motivated by this, we develop correlation and weighted correlation coefficients under the CIFS environment in which pairs of the membership degrees represent the two-dimensional information. Also, some of the desirable properties of it are investigated. Further, based on these measures, a multicriteria decision-making approach is presented under the CIFS environment. Two illustrative examples are taken to demonstrate the efficiency of the proposed approach and validate it by comparing their results with the several existing approaches' results.