The dominance relation on the class of continuous t-norms from an ordinal sum point of view

Authors:
Susanne Saminger;Peter Sarkoci;Bernard De Baets
Affiliations:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria;Department of Mathematics, IIEAM, Slovak University of Technology, Bratislava, Slovakia;Department of Applied Mathematics, Biometrics, and Process Control, Ghent University, Gent, Belgium
Venue:
TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
Year:
2006

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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 Łukasiewicz t-norm and the product t-norm.