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The Dominance Relation on the Class of Continuous T-Norms from an Ordinal Sum Point of View

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Theory and Applications of Relational Structures as Knowledge Instruments II

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4342))

Abstract

This paper addresses the relation of dominance on the class of continuous t-norms with a particular focus on continuous ordinal sum t-norms. Exactly, in this framework counter-examples to the conjecture that dominance is not only a reflexive and antisymmetric, but also a transitive relation could be found. We elaborate the details which have led to these results and illustrate them by several examples. In addition, to this original and comprehensive overview, we provide geometrical insight into dominance relationships involving prototypical Archimedean t-norms, the Ɓukasiewicz t-norm and the product t-norm.

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Author information

Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Altenbergerstrasse 69, A-4040, Linz, Austria

    Susanne Saminger

  2. Department of Mathematics, IIEAM, Slovak University of Technology, Radlinského 9, SK-81 368, Bratislava, Slovakia

    Peter Sarkoci

  3. Department of Applied Mathematics, Biometrics, and Process Control, Ghent University, Coupure links 653, B-9000, Gent, Belgium

    Bernard De Baets

Authors
  1. Susanne Saminger
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  2. Peter Sarkoci
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  3. Bernard De Baets
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

  2. National Institute of Telecommunications, Warsaw,  

    Ewa OrƂowska

  3. Institute for Software Technology, Department of Computing Science, UniversitĂ€t der Bundeswehr MĂŒnchen, 85577, Neubiberg, Germany

    Gunther Schmidt

  4. Faculté Polytechnique de Mons, Rue de Houdain 9, B-7000, Mons, Belgium

    Marc Roubens

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Saminger, S., Sarkoci, P., De Baets, B. (2006). The Dominance Relation on the Class of Continuous T-Norms from an Ordinal Sum Point of View. In: de Swart, H., OrƂowska, E., Schmidt, G., Roubens, M. (eds) Theory and Applications of Relational Structures as Knowledge Instruments II. Lecture Notes in Computer Science(), vol 4342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11964810_16

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  • DOI: https://doi.org/10.1007/11964810_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69223-2

  • Online ISBN: 978-3-540-69224-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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