Fuzzy differential equations: An approach via fuzzification of the derivative operator

In this paper we study fuzzy differential equations (FDEs) in terms of derivative for fuzzy functions, in a different way from the traditional Hukuhara derivative defined for set valued functions. The derivative we use is obtained by means of fuzzification of the classical derivative operator for standard functions. We discuss the relation of this approach to fuzzy differential inclusions (FDIs) and Hukuhara and strongly generalized derivatives. A theorem of existence of a solution is studied, with hypothesis similar to those assumed for FDIs. Some examples are explored in order to illustrate the theory.