Abstract As a preceding result, it has been shown that the dominance relation is not transitive on the set of strict triangular norms. This result has been achieved thanks to new results on Mulholland inequality. Recently, Saminger-Platz, De Baets, and De Meyer have introduced the generalized Mulholland inequality which characterizes the dominance on all continuous Archimedean triangular norms in an analogous way as does Mulholland inequality on the strict triangular norms. Based on these new results, the present paper shows that the dominance relation is not transitive on the set of nilpotent triangular norms and, consequently, on the set of continuous Archimedean triangular norms. This result is achieved by introducing a new sufficient condition under which a given function solves the generalized Mulholland inequality and by showing that the set of the functions that solve the inequality is not closed with respect to compositions.

中文翻译：

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连续阿基米德三角范数和广义穆赫兰不等式的优势

摘要 作为前面的结果，已经表明支配关系在严格三角范数的集合上是不传递的。这一结果的取得要归功于穆赫兰不等式的新结果。最近，Saminger-Platz、De Baets 和 De Meyer 引入了广义穆赫兰不等式，它以与严格三角范数上的穆赫兰不等式类似的方式表征了所有连续阿基米德三角范数上的优势。基于这些新结果，本文表明优势关系在幂零三角范数集上是不可传递的，因此，在连续阿基米德三角范数集上。