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Some Remarks on the Solutions to the Functional Equation I(x,y) = I(x,I(x,y)) for D-Operations

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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

This paper is devoted to the iterative functional equation I(x,y) = I(x,I(x,y)) for all x,y ∈ [0,1] where I denotes a fuzzy implication. This equation, that comes from a tautology in crisp logic, is revised from the results obtained in A. Xie and F. Qin (2010) Information Sciences, doi:10.1016/j.ins.2010.01.023, clarifying which kinds of continuous t-norms and t-conorms can be used in order to generate D-operations satisfying the mentioned equation.

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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

    Sebastià Massanet & Joan Torrens

Authors
  1. Sebastià Massanet
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  2. Joan Torrens
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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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Massanet, S., Torrens, J. (2010). Some Remarks on the Solutions to the Functional Equation I(x,y) = I(x,I(x,y)) for D-Operations. 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_70

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_70

  • 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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