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Negation Functions in the Set of Discrete Fuzzy Numbers

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 81))

Abstract

The aim of this paper is to build a strong negation \(\mathcal{N}\) on the bounded distributive lattice, \(\mathcal{A}_1^{L}\), of discrete fuzzy numbers whose support is a subset of consecutive natural numbers of the finite chain L = {0,1, ⋯ ,m}, from the only negation on L. Moreover, we obtain the \(\mathcal{N}\)-dual t-norm(t-conorm) of a \(\mathcal{T}(\mathcal{S})\) t-norm(t-conorm) on \(\mathcal{A}_1^{L}\).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Balearic Islands, 07122, Palma de Mallorca, Spain

    Jaume Casasnovas & J. Vicente Riera

Authors
  1. Jaume Casasnovas
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  2. J. Vicente Riera
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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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Casasnovas, J., Riera, J.V. (2010). Negation Functions in the Set of Discrete Fuzzy Numbers. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_41

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  • DOI: https://doi.org/10.1007/978-3-642-14058-7_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14057-0

  • Online ISBN: 978-3-642-14058-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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