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

  • Susanne Saminger
  • Peter Sarkoci
  • Bernard De Baets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4342)


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 Łukasiewicz t-norm and the product t-norm.


Dominance Relation Dominance Relationship Idempotent Element Triangular Norm Order Isomorphism 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Susanne Saminger
    • 1
  • Peter Sarkoci
    • 2
  • Bernard De Baets
    • 3
  1. 1.Department of Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria
  2. 2.Department of MathematicsIIEAM, Slovak University of TechnologyBratislavaSlovakia
  3. 3.Department of Applied Mathematics, Biometrics, and Process ControlGhent UniversityGentBelgium

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