Monotone functions that generate conditionally cancellative triangular subnorms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915733958557696 |
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| author | Chen, Meng Wang, Xue-ping |
| author_facet | Chen, Meng Wang, Xue-ping |
| contents | Let a function $F: [0,1]^2\rightarrow [0,1]$ be given by $F(x,y)= f^{(-1)}(T(f(x), f(y)))$ where $f :[0,1]\rightarrow [0,1]$ is a monotone function, $f^{(-1)}$ is the pseudo-inverse of $f$ and $T$ is a triangular norm. This article characterizes the monotone function $f$ satisfying that the function $F$ is a conditionally cancellative triangular subnorm completely. It finally answers an open problem posed by Mesiarová. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monotone functions that generate conditionally cancellative triangular subnorms Chen, Meng Wang, Xue-ping General Mathematics Let a function $F: [0,1]^2\rightarrow [0,1]$ be given by $F(x,y)= f^{(-1)}(T(f(x), f(y)))$ where $f :[0,1]\rightarrow [0,1]$ is a monotone function, $f^{(-1)}$ is the pseudo-inverse of $f$ and $T$ is a triangular norm. This article characterizes the monotone function $f$ satisfying that the function $F$ is a conditionally cancellative triangular subnorm completely. It finally answers an open problem posed by Mesiarová. |
| title | Monotone functions that generate conditionally cancellative triangular subnorms |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2601.10756 |