SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

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ARMAND ATEFEH; ALLAHVIRANLOO TOFIGH; GOUYANDEH ZEINAB

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2018 | Volume:15 | Issue:3 Page(s): 27-46

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Information Journal Paper

Title

SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

Author(s)

ARMAND ATEFEH | ALLAHVIRANLOO TOFIGH | GOUYANDEH ZEINAB | Issue Writer Certificate

Keywords

GENERALIZED HUKUHARA DERIVATIVEQ2

FUZZY LEIBNIZ’S RULEQ2

INTEGRATION BY PARTSQ2

FUZZY INTERMEDIATE VALUE THEOREMQ2

FUZZY MEAN VALUE THEOREM FOR INTEGRALQ2

MEAN VALUE THEOREM FOR GH-DERIVATIVEQ2

Abstract

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.

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APA: Copy

ARMAND, ATEFEH, ALLAHVIRANLOO, TOFIGH, & GOUYANDEH, ZEINAB. (2018). SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 15(3 ), 27-46. SID. https://sid.ir/paper/113253/en

Vancouver: Copy

ARMAND ATEFEH, ALLAHVIRANLOO TOFIGH, GOUYANDEH ZEINAB. SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2018;15(3 ):27-46. Available from: https://sid.ir/paper/113253/en

IEEE: Copy

ATEFEH ARMAND, TOFIGH ALLAHVIRANLOO, and ZEINAB GOUYANDEH, “SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 15, no. 3 , pp. 27–46, 2018, [Online]. Available: https://sid.ir/paper/113253/en

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