The Cauchy problem for complex fuzzy differential equations

    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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