Left-continuous pseudo-t-norms on modular lattices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917551479455744 |
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| author | He, Peng Wang, Xue-ping |
| author_facet | He, Peng Wang, Xue-ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left-continuous pseudo-t-norms on modular lattices He, Peng Wang, Xue-ping Representation Theory 03E72, 03B52, 03G10, 06B05 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. |
| title | Left-continuous pseudo-t-norms on modular lattices |
| topic | Representation Theory 03E72, 03B52, 03G10, 06B05 |
| url | https://arxiv.org/abs/2506.07567 |