Bidirectional approximate reasoning and pattern analysis based on a novel Fermatean fuzzy similarity metric

In various real-world scenarios, Fermatean fuzzy sets are commonly used to address fuzzy and uncertain challenges. The degree of similarity between Fermatean fuzzy sets is determined by computing the similarity between Fermatean fuzzy sets. The similarity metric can be used in a variety of activities, including "decision-making," "pattern recognition," "clustering analysis," and others. In this study, the three parameters of a Fermatean fuzzy set are taken into account to create a new Fermatean fuzzy similarity measure. The necessary axiomatic requirements of being a Fermatean fuzzy similarity measure are also established for the proposed similarity measure. Further, some new properties of the suggested measure are also discussed. Numerical experiments are used to test the validity of the suggested measure. To further demonstrate its effectiveness, the suggested measure is employed to resolve the bidirectional approximation reasoning and pattern recognition problems. The results of this study show that the suggested measure is a better and more precise measure that can overcome the shortcomings of most of the available measures.