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A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

Abstract

An interpretation of intuitionistic fuzzy sets is proposed based on random set theory and prototype theory. The extension of fuzzy labels are modelled by lower and upper random set neighbourhoods, identifying those element of the universe within an uncertain distance threshold of a set of prototypical elements. These neighbourhoods are then generalised to compound fuzzy descriptions generated as logical combinations of basic fuzzy labels. The single point coverage functions of these lower and upper random sets are then shown to generate lower and upper membership functions satisfying the min-max combination rules of interval fuzzy set theory, the latter being isomophic to intuitionistic fuzzy set theory.

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Author information

Authors and Affiliations

  1. Department of Engineering Mathematics, University of Bristol, Bristol, UK

    Jonathan Lawry

Authors
  1. Jonathan Lawry
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

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Lawry, J. (2010). A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_65

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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