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arXiv · 2506.07567

Left-continuous pseudo-t-norms on modular lattices

Peng He·Xue-ping Wang
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Abstract

This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint complete lattices. Then, we define the $1$-distributivity of a lattice, which is applied for characterizing a complete atomistic lattice that has a left-continuous pseudo-t-norm. We also describe the forbidden structures of a finite modular lattice that is a $1$-distributive lattice, which is used for representing a kind of finite planar modular lattices that have left-continuous pseudo-t-norms.

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BibTeXRIS

Peng He, Xue-ping Wang. 2025-06-09. Left-continuous pseudo-t-norms on modular lattices. https://doi.org/10.1016/j.fss.2026.109847

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