A spherical fuzzy set is a generalization of picture fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets in which the square sum of the membership, non-membership, and neutrality values is at most one. The correlation coefficient is a crucial tool in fuzzy/non-standard fuzzy theory and has been applied in various fields such as clustering, pattern recognition, medical diagnosis, decision-making, etc. The existing correlation coefficients for spherical fuzzy sets give only the correlation degree and do not express the nature or direction of correlation between the spherical fuzzy sets. So, in this study, we propose two correlation coefficients for spherical fuzzy sets, which not only give the strength of correlation between two spherical fuzzy sets but also tell us whether the two spherical fuzzy sets are positively correlated or negatively correlated. We also discuss several properties of these correlation coefficients. We apply these correlation coefficients to solve a pattern recognition problem in the spherical fuzzy environment and compare the results with some existing measures.
