Generalized triparametric correlation coefficient for Pythagorean fuzzy sets with application to MCDM problems

Pythagorean fuzzy set (PFS) is an advanced version of intuitionistic fuzzy set which generalizes fuzzy set. Consequently, PFS has a better applicative expression in real-life decision-making (RLDM) or multicriteria decision-making (MCDM) problems due to its capacity to curb uncertainties embedded in decision making. Correlation coefficient is a significant measuring tool applicable to solving RLDM/MCDM problems via Pythagorean fuzzy environment approach. The main aim of this paper is to reexamine Garg’s correlation coefficient for PFSs and generalize it for a better output in resolving MCDM problems. The axiomatic description of correlation coefficient for PFSs is proposed, and the generalized triparametric correlation coefficient for PFSs is characterized with some number of results. Numerical verification of the proposed correlation coefficient is given to validate the preeminence of the generalized correlation coefficient for PFSs over Garg’s approach. Lastly, some MCDM problems such as pattern recognition problem (e.g., classification of mineral fields) and diagnostic medicine in the framework of Pythagorean fuzzy pairs are discussed with the aid of the novel correlation coefficient. This proposed measuring tool could be exploited in other MCDM problems via object-oriented approach.