发表机构
Faculty of Science, Huzhou Normal University（湖州师范学院理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整刻画了连续t-余范数弱支配连续t-范数的条件，通过归结为阿基米德分量并用加法生成元表达，统一覆盖严格与幂零情形。
AI 中文摘要
聚合算子理论中，聚合算子的弱支配性，特别是三角范数（t-范数）与三角余范数（t-余范数）之间的弱支配性，已引起广泛关注。虽然对于阿基米德情形和连续情形已获得若干刻画，但连续t-余范数对连续t-范数的弱支配性的一般准则仍有待完全阐明。本文给出了连续t-余范数弱支配连续t-范数的完整刻画。我们首先将序数和算子的情形归结为其单个阿基米德分量的问题，然后完全用这些分量的加法生成元来表达弱支配条件。我们的方法统一涵盖了严格情形和幂零情形，并将阿基米德算子的已知结果作为特例加以恢复。
英文摘要
The weak dominance of aggregation operators, particularly between triangular norms (t-norms) and triangular conorms (t-conorms), has attracted considerable attention in aggregation operator theory. While several characterizations have been obtained for Archimedean and continuous cases, a general criterion for continuous t-conorms over continuous t-norms remains to be fully clarified. In this paper, we provide a complete characterization of a continuous t-conorm weakly dominating a continuous t-norm. We first reduce the problem for ordinal sum operators to that for their single Archimedean components, and then express the weak dominance condition entirely in terms of the additive generators of these components. Our approach covers both strict and nilpotent cases uniformly, and recovers the known results for Archimedean operators as a special case.
