Some new Pythagorean fuzzy correlation techniques via statistical viewpoint with applications to decision-making problems

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Abstract
Pythagorean fuzzy set is a reliable technique for soft computing because of its ability to curb indeterminate data when compare to intuitionistic fuzzy set. Among the several measuring tools in Pythagorean fuzzy environment, correlation coefficient is very vital since it has the capacity to measure interdependency and interrelationship between any two arbitrary Pythagorean fuzzy sets (PFSs). In Pythagorean fuzzy correlation coefficient, some techniques of calculating correlation coefficient of PFSs (CCPFSs) via statistical perspective have been proposed, however, with some limitations namely; (i) failure to incorporate all parameters of PFSs which lead to information loss, (ii) imprecise results, and (iii) less performance indexes. Sequel, this paper introduces some new statistical techniques of computing CCPFSs by using Pythagorean fuzzy variance and covariance which resolve the limitations with better performance indexes. The new techniques incorporate the three parameters of PFSs and defined within the range [-1, 1] to show the power of correlation between the PFSs and to indicate whether the PFSs under consideration are negatively or positively related. The validity of the new statistical techniques of computing CCPFSs is tested by considering some numerical examples, wherein the new techniques show superior performance indexes in contrast to the similar existing ones. To demonstrate the applicability of the new statistical techniques of computing CCPFSs, some multi-criteria decision-making problems (MCDM) involving medical diagnosis and pattern recognition problems are determined via the new techniques.

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