Kybernetika 42 no. 3, 337-350, 2006

On the dominance relation between ordinal sums of conjunctors

Susanne Saminger, Bernard De Baets and Hans De Meyer

Abstract:

This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.