A Novel Correlation Coefficient for Spherical Fuzzy Sets and Its Application in Pattern Recognition, Medical Diagnosis, and Mega Project Selection

Abstract

The correlation coefficient (CC) is a statistical measure that is very useful to quantify the strength and direction of the relationship between two variables, processes, or sets. The primary objective of this paper is to propose a novel CC explicitly tailored for spherical fuzzy sets (SFSs), aiming to address the limitations and drawbacks associated with existing CCs. Our approach employs statistical concepts to quantify the correlation between variables and datasets within the context of SFSs. We formulate our proposed CC for SFSs by incorporating variance and covariance as fundamental components. This innovative approach not only accurately quantifies the degree of correlation between two SFSs but also characterizes the nature of their relationship, whether it is positive, neutral, or negative. As a result, our CC yields numerical values within the range of [−1, 1]. In contrast, existing methods focus solely on measuring the degree of association between two SFSs and are unable to differentiate the nature of the relationship, especially in cases of inverse correlation. We conduct a comparison to evaluate the efficiency of our proposed scheme in comparison to existing techniques, using numerical examples to showcase the dominance of our method. The comparative results indicate that our proposed approach effectively addresses the limitations of existing methods and produces more reliable and precise results. Furthermore, we applied our method to address three real-world challenges in pattern recognition, medical diagnosis, and mega-project selection, demonstrating its practicality, advantages, and usefulness.