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Fuzzy Relational Images in Computer Science

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Relational Methods in Computer Science (RelMiCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2561))

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Abstract

Relations appear in many fields of mathematics and computer science. In classical mathematics these relations are usually crisp, i.e. two objects are related or they are not. However, many relations in real-world applications are intrinsically fuzzy, i.e. objects can be related to each other to a certain degree.

With each fuzzy relation, different kinds of fuzzy relational images can be associated, all with a very practical interpretation in a wide range of application areas. In this paper we will explicite the formal link between well known direct and inverse images of fuzzy sets under fuzzy relations on one hand, and different kinds of compositions of fuzzy relations on the other. Continuing from this point of view we are also able to define a new scale of so-called double images. The wide applicability in mathematics and computer science of all these fuzzy relational images is illustrated with several examples.

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Author information

Authors and Affiliations

  1. Fuzziness and Uncertainty Modelling Research UnitDepartment of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000, Gent, Belgium

    Mike Nachtegael, Martine De Cock, Dietrich Van der Weken & Etienne E. Kerre

Authors
  1. Mike Nachtegael
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  2. Martine De Cock
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  3. Dietrich Van der Weken
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  4. Etienne E. Kerre
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Editor information

Editors and Affiliations

  1. Tilburg University, P.O. Box 90153, 5000, LE Tilburg, The Netherlands

    Harrie C. M. de Swart

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© 2002 Springer-Verlag Berlin Heidelberg

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Nachtegael, M., De Cock, M., Van der Weken, D., Kerre, E.E. (2002). Fuzzy Relational Images in Computer Science. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_10

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  • DOI: https://doi.org/10.1007/3-540-36280-0_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00315-1

  • Online ISBN: 978-3-540-36280-7

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