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Fuzzy Sets and Fuzzy Partitions

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Information and Classification

Part of the book series: Studies in Classification, Data Analysis and Knowledge Organization ((STUDIES CLASS))

Abstract

In this paper some connections between a characterization of fuzzy sets and a characterization of fuzzy partitions are explored. We extend the notion of α-level set and sharpness of fuzzy sets to fuzzy partitions. Then we define α-level equivalence and relation of sharpness on the set of all fuzzy partitions of a finite set of objects into k clusters. We define sharpnesshood and complementhood of fuzzy partitions and then we show how to find the complement of a fuzzy partition.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&I University, Kingsville, TX, 78363, USA

    Slavka Bodjanova

Authors
  1. Slavka Bodjanova
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Mathematische Methoden der Wirtschaftswissenschaften, Universität Augsburg, Universitätsstr. 2, D-86135, Augsburg, Germany

    Otto Opitz

  2. Forschungsinstitut für Kinderernährung, Heinstück 11, D-44225, Dortmund, Germany

    Berthold Lausen

  3. Abteilung für Medizinische Informatik, Universitäts-Klinikum Freiburg, Stefan-Meier-Str. 26, D-79104, Freiburg, Germany

    Rüdiger Klar

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© 1993 Springer-Verlag Berlin · Heidelberg

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Cite this paper

Bodjanova, S. (1993). Fuzzy Sets and Fuzzy Partitions. In: Opitz, O., Lausen, B., Klar, R. (eds) Information and Classification. Studies in Classification, Data Analysis and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50974-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-50974-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56736-3

  • Online ISBN: 978-3-642-50974-2

  • eBook Packages: Springer Book Archive

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