Constructing left-continuous triangular norms on complete lattices

Peng He; Xue-ping Wang

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arXiv · 2601.07146

Constructing left-continuous triangular norms on complete lattices

Peng He·Xue-ping Wang

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Abstract

This article focuses on the construction of left-continuous t-norms on complete lattices. The concepts of $\mathfrak{f}$-mappings and weak $\mathfrak{f}$-mappings on complete lattices are first introduced, respectively. They are then applied to establish the following key results: weak $\mathfrak{f}$-mappings are used to induce left-continuous t-subnorms; $\mathfrak{f}$-mappings are used to generate left-continuous t-norms whenever the top element $1$ of the complete lattice is a completely join-irreducible element. Finally, some necessary and sufficient conditions are provided for an operator constructed by the ordinal sum of a series of annihilating binary operators being a left-continuous t-norm on a complete lattice.

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Peng He, Xue-ping Wang. 2026-01-12. Constructing left-continuous triangular norms on complete lattices. https://arxiv.org/abs/2601.07146

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