Structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms

Zhenyu Xiu; Zhengyuan Si

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arXiv · 2511.06206

Structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms

Zhenyu Xiu·Zhengyuan Si

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Abstract

In this paper, we provide some structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms, subject to certain constraints on the closure operators and t-subnorms. Importantly, these constraints are shown to be both sufficient and necessary. That is, the proposed methods reveal clear relationships between the structure of the resulting uninorms and the properties of the underlying components. Meanwhile, we present the degenerate cases of the aforementioned results, which are constructed using special closure operators and t-subnorms. Some of these cases correspond to well-known results documented in the literature. Moreover, the dual constructions of uninorms on bounded lattices, based on t-norms, interior operators and t-superconorms, are presented simultaneously.

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BibTeX RIS

Zhenyu Xiu, Zhengyuan Si. 2025-11-09. Structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms. https://arxiv.org/abs/2511.06206

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