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Dual Representable Aggregation Functions and Their Derived S-Implications

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Computational Intelligence for Knowledge-Based Systems Design (IPMU 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6178))

Abstract

In this paper dual representable aggregation functions (DRAF’s) are introduced and studied. After giving a representation theorem for them, it is proved that they can be viewed as a non-associative generalization of nilpotent t-conorms, some basic properties are proved and some examples are given. On the other hand, using DRAF’s a new kind of strong implications are derived and some usual properties are studied for this new class of implications. In particular, it is shown that they have an easy structure always divided into three parts depending on the strong negation.

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Author information

Authors and Affiliations

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

    Isabel Aguiló, Marc Carbonell, Jaume Suñer & Joan Torrens

Authors
  1. Isabel Aguiló
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  2. Marc Carbonell
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  3. Jaume Suñer
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  4. Joan Torrens
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032, Marburg, Germany

    Eyke Hüllermeier

  2. Fakultät Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, Otto-Hahn-Str. 4, 44227, Dortmund, Germany

    Frank Hoffmann

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Aguiló, I., Carbonell, M., Suñer, J., Torrens, J. (2010). Dual Representable Aggregation Functions and Their Derived S-Implications. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_42

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  • DOI: https://doi.org/10.1007/978-3-642-14049-5_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14048-8

  • Online ISBN: 978-3-642-14049-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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