Fuzzy calculus via extension of the derivative and integral operators and fuzzy differential equations

Abstract

We define the concepts of derivative and integral of fuzzy functions using the extension principle of Zadeh on the corresponding classical operators. Here are some of its properties and we articulate a version of the Fundamental Theorem of Calculus for fuzzy functions and ensure the existence of a solution of fuzzy initial value problem under certain conditions. A method of solving fuzzy initial value problem is presented and an application of a decay model is solved and interpreted within a fuzzy context.