Atefeh Armand - Young Researchers and Elites Club, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran
Tofigh Allahviranloo - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Zienab Gouyandeh - Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran

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.

Generalized Hukuhara derivative, Fuzzy Leibniz&#۰۳۹;s rule, Integration by parts, Fuzzy intermediate value theorem, Fuzzy mean value theorem for integral, Mean value theorem for gH-derivative