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

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 Lukasiewicz t-norm and the product t-norm. © Springer-Verlag Berlin Heidelberg 2006.