Some new correlation coefficients of picture fuzzy sets with applications

Picture fuzzy set (PFS) is an important tool for handling uncertainty and vagueness, particularly in situations that require more answers of the type "yes," "no," "abstain" and "refusal." Correlation coefficient of picture fuzzy sets (PFSs) is an essential measure in picture fuzzy set theory and has a lot of applications in many areas, such as "decision-making," "medical diagnosis," "pattern recognition" and "clustering analysis". In this article, two correlation coefficients of PFSs are introduced along with some of their properties. These correlation coefficients of PFSs are better than existing ones and effective in expressing the nature of correlation (positive or negative correlation). We also show the applications and advantages of the proposed picture fuzzy correlation coefficients over some existing methods in pattern recognition, medical diagnosis and clustering with the help of illustrative examples.