A three-way Pythagorean fuzzy correlation coefficient approach and its applications in deciding some real-life problems

Correlation coefficient (CC) is a reliable information measure for measuring interrelationship between Pythagorean fuzzy sets (PFSs). Some approaches for calculating CC of PFSs have been considered. These hitherto approaches assess only the strength of relationship between PFSs, and are described within the interval [0, 1]. This paper proposes a three-way approach for the computation of CC between PFSs by using the concepts of variance and covariance, respectively. This new approach is defined within the interval [-1,1] akin to classical statistics, shows the strength of relationship between the considered PFSs and indicates whether the PFSs are either positively or negatively correlated. By including the three conventional parameters of PFSs in the proposed technique, the possibility of error due to information leakage is reasonably minimized The new technique is validated with some theoretical results to show its suitability as reliable information measure. Some numerical examples are considered to show the edges of the new methods over similar methods. From the comparative analysis, the proposed methods of computing CCPFSs give more reliable and reasonable results compare to similar existing methods as presented in Table 13. Certain decision-making problems involving recognition of patterns and diagnostic medicine are resolved with the aid of the new method. The three-way technique of computing correlation coefficient between PFSs can solve decision-making problems that are multi-attributes in nature.