A study of weak dominance for t-conorms and null-norms of ordinal sums

Xiaodong Hou; Nan Zhang; Jiajia Fan; Xiaodong Hou; Nan Zhang; Jiajia Fan

doi:10.3934/math.2026984

AIMS Mathematics

2026, Volume 11, Issue 8: 24379-24396. doi: 10.3934/math.2026984

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Research article Topical Sections

A study of weak dominance for t-conorms and null-norms of ordinal sums

1.
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
2.
Taishan University of Science and Technology, Taian 271038, China

Received: 25 March 2026 Revised: 17 June 2026 Accepted: 29 July 2026 Published: 10 August 2026
MSC : 39B52, 39B55

This study focuses on the weak dominance between t-conorms and nullnorms given by the following inequality:
$ \begin{equation*} S(N(x, y), z) \geq N(S(x, z), y), \quad x, y, z\in [0, 1], \end{equation*} $
where $ N $ is a nullnorm and $ S $ is a t-conorm. The paper mainly discusses the case where $ N $ has an ordinal sum structure, its underlying operators are Archimedean, and $ S $ is Archimedean. The established relations are proved through the concavity and convexity of functions constructed from the additive generators corresponding to the underlying operators.
- weak dominance,
- nullnorms,
- t-conorms,
- ordinal sum,
- convex,
- concave
Citation: Xiaodong Hou, Nan Zhang, Jiajia Fan. A study of weak dominance for t-conorms and null-norms of ordinal sums[J]. AIMS Mathematics, 2026, 11(8): 24379-24396. doi: 10.3934/math.2026984

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Abstract

This study focuses on the weak dominance between t-conorms and nullnorms given by the following inequality:

$ \begin{equation*} S(N(x, y), z) \geq N(S(x, z), y), \quad x, y, z\in [0, 1], \end{equation*} $

where $ N $ is a nullnorm and $ S $ is a t-conorm. The paper mainly discusses the case where $ N $ has an ordinal sum structure, its underlying operators are Archimedean, and $ S $ is Archimedean. The established relations are proved through the concavity and convexity of functions constructed from the additive generators corresponding to the underlying operators.

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