Construction of distance measure for Fermatean fuzzy sets and its application in educational assessment and medical diagnosis

Fermatean fuzzy sets (FFSs), an updated, expanded version of intuitionistic fuzzy sets (IFSs), are effective tools for expressing uncertainty and ambiguity in complicated issues. The distance measure is a crucial tool for illustrating the differences between two FFSs while dealing with Fermatean fuzzy information. It is currently unclear how to precisely calculate the distinction between two FFSs. We provide a novel distance measurement method for FFSs in this study. Then, we show that the chosen distance measurement method satisfies the distance function's axiomatic requirements. The presented distance measure is then evidenced with numerical examples to show that it is more accurate and reasonable than the Mizumoto(I) distance measure, Robert(I) distance measure, Robert(II) distance measure, Mizumoto(II) distance measure, Hellinger distance, Euclidean distance (ED) measure and triangle divergence distance measure, which is capable of overcoming the counter-intuitive circumstance. In addition, we successfully use the proposed distance measure approach to handle pattern recognition difficulties, educational assessment issues, and medical diagnosis issues in a fuzzy Fermatean environment. The experimental findings show how effectively the suggested distance measure method can handle real-world applications in a fuzzy Fermatean environment.