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

fYear

2012

fDate

6-8 Aug. 2012

Firstpage

1

Lastpage

5

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American

Conference_Location

Berkeley, CA

ISSN

pending

Print_ISBN

978-1-4673-2336-9

Electronic_ISBN

pending

Type

conf

DOI

10.1109/NAFIPS.2012.6290965

Filename

6290965