Note on additive generator pairs of overlap and grouping functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912418566766592 |
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| author | Liang, Li-zhi Wang, Xue-ping |
| author_facet | Liang, Li-zhi Wang, Xue-ping |
| contents | In this article, we deeply reveal the relationship between functions $θ$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($θ$,$\vartheta$). Then we characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $θ$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on additive generator pairs of overlap and grouping functions Liang, Li-zhi Wang, Xue-ping Representation Theory In this article, we deeply reveal the relationship between functions $θ$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($θ$,$\vartheta$). Then we characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $θ$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions. |
| title | Note on additive generator pairs of overlap and grouping functions |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.01221 |