A generalization of the Mulholland inequality for continuous Archimedean t-norms

It is well known that dominance between strict t-norms is closely related to the Mulholland inequality, which can be seen as a generalization of the Minkowski inequality. However, strict t-norms constitute only one part of the class of continuous Archimedean t-norms, the basic elements from which all continuous t-norms are composed. In this paper, dominance between continuous Archimedean t-norms is shown to be related to a generalization of the Mulholland inequality. We provide sufficient and necessary conditions for its fulfillment.