A novel Pythagorean fuzzy correlation coefficient based on Spearman's technique of correlation coefficient with applications in supplier selection process

Abstract

A Pythagorean fuzzy correlation coefficient (PFCC) is a reliable approach for eliminating ambiguity during the measure of relationships. Numerous Pythagorean fuzzy correlation coefficient methods (PFCCMs) have been constructed using Pearson's correlation coefficient technique. In this study, anew PFCCM is constructed based on Spearman's correlation coefficient to eliminate all possible uncertainties that may impede decision-makers from making a dependable selection. To validate the construction of anew PFCCM, we examine the existing PFCCMs and pinpoint their inadequacies. Among the extant PFCCMs, one approach was constructed through Spearman's correlation coefficient but it does not takes into cognizance the properties of the PFSs. In addition, it sometimes fails the axiomatic conditions of the PFCC, and yields invalid result for PFSs that are defined on a singleton set. These setbacks justify the construction of anew Spearman's correlation coefficient-like PFCCM, which is shown to overcome the limitations of the extant PFCCMs. Equally, the strength of the new PFCCM is verified by some theoretical results, and it fulfills the conditions of PFCC. Additionally, the use of the novel PFCCM is discussed in the solution of supplier selection problems to eliminate supplier selection ambiguity through the multiple criteria decision-making (MCDM) approach. To unarguably show the intrinsic worth of the new PFCCM, the effectiveness of the new PFCCM is compared with the existing PFCCMs and it is observed that the new PFCCM is reliable, consistent and precise, and in the same way satisfies the axioms of the PFCC. In particular, the existing Spearman's PFCCM yields cc in Example 4, while the new PFCCM produces 0.7603, which justifies the construction of anew Spearman's PFCCM. Finally, it is found that the new approach can suitably handle the hesitancies associated with the art of selection.