When is the operation $τ_{T,L}$ a triangle function on $\Del^+$?
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911245865582592 |
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| author | Lai, Hongliang Luo, Mengyu Zhang, Jie |
| author_facet | Lai, Hongliang Luo, Mengyu Zhang, Jie |
| contents | This paper resolves an open problem posed by Schweizer and Sklar in 1983. We establish that the binary operation $\tauTL$ is a triangle function on $\Delp$ if and only if the following three conditions hold: (a) $L$ is a continuous t-conorm on $[0, \infty]$ satisfying $(LCS)$; (b) $T$ is a t-norm on $[0, 1]$; and (c) $T$ is weakly left continuous, with left continuity required when $L$ is non-Archimedean. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When is the operation $τ_{T,L}$ a triangle function on $\Del^+$? Lai, Hongliang Luo, Mengyu Zhang, Jie General Topology This paper resolves an open problem posed by Schweizer and Sklar in 1983. We establish that the binary operation $\tauTL$ is a triangle function on $\Delp$ if and only if the following three conditions hold: (a) $L$ is a continuous t-conorm on $[0, \infty]$ satisfying $(LCS)$; (b) $T$ is a t-norm on $[0, 1]$; and (c) $T$ is weakly left continuous, with left continuity required when $L$ is non-Archimedean. |
| title | When is the operation $τ_{T,L}$ a triangle function on $\Del^+$? |
| topic | General Topology |
| url | https://arxiv.org/abs/2510.26439 |