Additive generator pairs of overlap functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917115760476160 |
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| author | Liang, Li-zhi Wang, Xue-ping |
| author_facet | Liang, Li-zhi Wang, Xue-ping |
| contents | Let $θ:[0,1]\rightarrow[-\infty,+\infty]$ be a function with both $θ(x^{-})$ and $θ(x^{+})$ existing for every $x\in [0,1]$ and $\vartheta:[-\infty,+\infty]\rightarrow[-\infty,+\infty]$ be a function. In this article we completely characterize the pair $(θ,\vartheta)$ for the bivariate function $O_{θ,\vartheta}: [0,1]^{2}\rightarrow[0,1]$ given by $$O_{θ,\vartheta}(x,y)=\vartheta(θ(x)+θ(y))$$ being an overlap function. In particular, we give analytical expressions of some transformations for the pair $(θ,\vartheta)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additive generator pairs of overlap functions Liang, Li-zhi Wang, Xue-ping General Mathematics Let $θ:[0,1]\rightarrow[-\infty,+\infty]$ be a function with both $θ(x^{-})$ and $θ(x^{+})$ existing for every $x\in [0,1]$ and $\vartheta:[-\infty,+\infty]\rightarrow[-\infty,+\infty]$ be a function. In this article we completely characterize the pair $(θ,\vartheta)$ for the bivariate function $O_{θ,\vartheta}: [0,1]^{2}\rightarrow[0,1]$ given by $$O_{θ,\vartheta}(x,y)=\vartheta(θ(x)+θ(y))$$ being an overlap function. In particular, we give analytical expressions of some transformations for the pair $(θ,\vartheta)$. |
| title | Additive generator pairs of overlap functions |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2512.01154 |