Constructing left-continuous triangular norms on complete lattices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915722670637056 |
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| author | He, Peng Wang, Xue-ping |
| author_facet | He, Peng Wang, Xue-ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructing left-continuous triangular norms on complete lattices He, Peng Wang, Xue-ping General Mathematics 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. |
| title | Constructing left-continuous triangular norms on complete lattices |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2601.07146 |