On weak dominance of t-conorms over t-norms
Abstract
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.
Related
- Measure Convergence under Weak Domination for Unitarily Invariant Norms on Finite von Neumann Algebras
- Harmonic Norms on Quiver Representations over Non-Archimedean Fields
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- Pointwise function spaces over compacta are not weak Banach spaces
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BibTeX
@misc{li2026weak,
title = {{On weak dominance of t-conorms over t-norms}},
author = {Shuangquan Li and Yao Ouyang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11150},
eprint = {2609.11150},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11150},
}
RIS
TY - UNPB
TI - On weak dominance of t-conorms over t-norms
AU - Shuangquan Li
AU - Yao Ouyang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11150
UR - https://arxiv.org/abs/2609.11150
AB - 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.
ER -