Title

The Cauchy Problem For Complex Fuzzy Differential Equations

Keywords

Cauchy problem; Complex fuzzy differential equations; Complex-valued grades of membership; Existence theorem; Uniqueness theorem

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 Hölder continuous or Lipschitz continuous response functions. © 2013 Elsevier B.V.

Publication Date

6-16-2014

Publication Title

Fuzzy Sets and Systems

Volume

245

Number of Pages

18-29

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.fss.2013.11.001

Socpus ID

84899483002 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84899483002

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