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

Abstract

Set Pair Analysis (SPA) is an updated theory of dealing with uncertainty, which overlaps with other theories of uncertainty such as probability, vague, fuzzy, and Intuitionistic Fuzzy Set (IFS). Considering the fact that the correlation coefficient plays an important role during a decision-making process, after revealing the weakness of the existing correlation coefficients between the IFSs, this study proposes a novel correlation coefficient and weighted correlation coefficients formulation to measure the relative strength of different IFSs. To do so, firstly, corresponding to each intuitionistic fuzzy number, the connection number of the SPA theory is formulated in the form of the identity, discrepancy, and contrary degrees; moreover, measurements of the novel correlation coefficient are defined. Pairs of identity, discrepancy, and contrary of the connection number are taken as a vector representation during the formulation. Lastly, a decision-making approach based on the proposed measures is presented, illustrated by two numerical examples in pattern recognition and medical diagnosis.