Differential calculus of fermatean fuzzy functions: Continuities, derivatives, and differentials

Abstract

Fermatean fuzzy sets are an effective way to handle uncertainty and vagueness by expanding the spatial scope of membership and nonmembership of the intuitionistic fuzzy set and the Pythagorean fuzzy set. However, existing studies only analyzed the discrete information and neglected the continuous state of Fermatean fuzzy sets. In this paper, we investigated the properties of continuous Fermatean fuzzy information by firstly proposing Fermatean fuzzy functions, then defining the subtraction and division operations of Fermatean fuzzy functions and discussing their properties. Further, we examined the continuity, deriva-tives, and differentials of Fermatean fuzzy functions. Effective approximate calculations regarding nonlinear problems in the Fermatean fuzzy environment were provided, and some examples were presented to verify the feasibility and effectiveness of approximate calculations using the Fermatean fuzzy functions.