Applicability of a novel Pythagorean fuzzy correlation coefficient in medical diagnosis, clustering, and classification problems

A Pythagorean fuzzy set outperforms fuzzy and intuitionistic fuzzy sets in solving uncertain issues. For comparing Pythagorean fuzzy sets, compatibility indices such as distance, similarity, correlation, divergence, etc. are essential. The sole compatibility metric that reveals the nature of the relationship between the Pythagorean fuzzy sets is the correlation coefficient. There are many applications for the correlation coefficient in decision-making, pattern analysis, medical diagnosis, and other areas. The novel coefficient of correlation for Pythagorean fuzzy sets that we have proposed in this study provides both the nature (positive or negative) and level of the correlation between two Pythagorean fuzzy sets. We also compared the proposed correlation coefficient to all previously calculated Pythagorean fuzzy correlation coefficients. The utility of the suggested metrics has been demonstrated in classification, medical diagnosis, and clustering problems employing Pythagorean fuzzy data. All of the Pythagorean fuzzy correlation coefficients that are currently in use have been compared to the findings of the proposed measure. In classification problems, the proposed metric has a high level of confidence.