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Fuzzy Topologies Induced by Fuzzy Relation Based Modifiers

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Book cover Computational Intelligence. Theory and Applications (Fuzzy Days 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2206))

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Abstract

In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to the recently introduced general closure and opening operators based on arbitrary fuzzy relations.

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Author information

Authors and Affiliations

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

    Martine De Cock & E. E. Kerre

Authors
  1. Martine De Cock
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  2. E. E. Kerre
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Editor information

Editors and Affiliations

  1. Computer Science I, University of Dortmund, 44221, Dortmund, Germany

    Bernd Reusch

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© 2001 Springer-Verlag Berlin Heidelberg

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De Cock, M., Kerre, E.E. (2001). Fuzzy Topologies Induced by Fuzzy Relation Based Modifiers. In: Reusch, B. (eds) Computational Intelligence. Theory and Applications. Fuzzy Days 2001. Lecture Notes in Computer Science, vol 2206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45493-4_28

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  • DOI: https://doi.org/10.1007/3-540-45493-4_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42732-2

  • Online ISBN: 978-3-540-45493-9

  • eBook Packages: Springer Book Archive

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