Title :
Fuzzy calculus via extension of the derivative and integral operators and fuzzy differential equations
Author :
Gomes, Luciana T. ; Barros, Laécio C.
Author_Institution :
Dept. of Appl. Math., Univ. of Campinas, Campinas, Brazil
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.
Keywords :
calculus; differential equations; fuzzy set theory; initial value problems; radioactive decay schemes; Zadeh extension principle; calculus fundamental theorem; derivative operators; fuzzy calculus; fuzzy differential equations; fuzzy initial value problem; integral operators; radioactive decay model; Context; Differential equations; Fuzzy sets; Integral equations; Mathematical model; Uncertainty;
Conference_Titel :
Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American
Conference_Location :
Berkeley, CA
Print_ISBN :
978-1-4673-2336-9
Electronic_ISBN :
pending
DOI :
10.1109/NAFIPS.2012.6290965
