Dominance on strict triangular norms and Mulholland inequality

This paper is devoted to the question of transitivity of the dominance relation defined on the set of strict triangular norms and to the connection between dominance and Mulholland inequality. A summary of the results reached in this field is given and a new result for the strict triangular norms of Family 19 is shown. Further, some parametric classes of solutions of Mulholland inequality, that do not comply with the Mulholland's condition, are presented and, finally, it is shown that the dominance relation is, in general, not transitive on the set of strict triangular norms.