SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS
نویسندگان
1 Young Researchers and Elites Club, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
doi
10.22111/ijfs.2018.3948چکیده
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.
