SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

In this paper, we study fuzzy calculus in two main branches differential and integral. Some rules for finding limit and gH-derivative of gH- difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating gH-derivative of a composite function. Two techniques namely, Leibniz’s rule and integration by parts are introduced for fuzzy integrals. Furthermore, we prove three essential theorems such as a fuzzy intermediate value theorem, fuzzy mean value theorem for integral and mean value theorem for gH-derivative. We derive a Bolzano’s theorem, Rolle’s theorem and some properties for gH-differentiable functions. To illustrate and explain these rules and theorems, we have provided several examples in details.