Title

The Cauchy problem for complex fuzzy differential equations

Authors

Authors

D. Karpenko; R. A. Van Gorder;A. Kandel

Comments

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Abbreviated Journal Title

Fuzzy Sets Syst.

Keywords

Complex-valued grades of membership; Complex fuzzy differential; equations; Cauchy problem; Existence theorem; Uniqueness theorem; EXISTENCE; SETS; UNIQUENESS; THEOREM; SPACES; LOGIC; Computer Science, Theory & Methods; Mathematics, Applied; Statistics &; Probability

Abstract

We discuss the existence of a solution to the Cauchy problem for fuzzy differential equations that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definitions of complex fuzzy sets and discuss entailed results which parallel those of regular fuzzy numbers. We then give two existence results relevant to the Cauchy problem for fuzzy differential equations in the case of bounded integral operators. These results require either Holder continuous or Lipschitz continuous response functions. (C) 2013 Elsevier B.V. All rights reserved.

Journal Title

Fuzzy Sets and Systems

Volume

245

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

18

Last Page

29

WOS Identifier

WOS:000336470500002

ISSN

0165-0114

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