Fermatean Fuzzy Type a Three-Way Correlation Coefficients

In challenging decision-making circumstances, tools like aggregation operators and information measures are routinely used. Using correlation coefficient (KK)’s estimate of the amount of reliance between two sets is another way to decide which choice is better. There are a few methods for figuring out the KK of Fermatean fuzzy sets (FFSs). These previous methodologies, which are specified between \([0, 1]\), simply evaluate the strength of the link between FFSs. This study, using the notions of variance and covariance, respectively, provides a three-way method for computing the KKs between FFSs. The strength of the association between the considered FFSs is demonstrated by this novel approach, which is defined inside the interval \([-1, 1]\) similar to standard statistics, and it identifies whether the FFSs are positively or negatively associated. The potential of inaccuracy owing to information leakage is reasonably mitigated by the suggested technique’s inclusion of the three traditional FFSs parameters. To demonstrate the new technique’s usefulness as an accurate information measure, several theoretical results will be used to validate it. The advantages of the new methods over comparable methods will be demonstrated using a few numerical examples. With the help of the novel approach, several decision-making issues involving pattern recognition and diagnostic medicine will be handled. Multi-attribute decision-making issues can be resolved using the three-way technique for determining the correlation coefficient between FFSs.