Associativity of two-place functions generated by left continuous monotone functions and other properties
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912463809675264 |
|---|---|
| author | Chen, Meng Wang, Xue-ping |
| author_facet | Chen, Meng Wang, Xue-ping |
| contents | This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function with neutral element in $[0,\infty]$, $t: [0,1]\rightarrow [0,\infty]$ is a left continuous monotone function and $t^{[-1]}:[0,\infty]\rightarrow[0,1]$ is the weak pseudo-inverse of $t$. It shows that the associativity of the function $T$ depends only on properties of the range of $t$. Moreover, it investigates the idempotence, the limit property, the conditional cancellation law and the continuity of the function $T$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Associativity of two-place functions generated by left continuous monotone functions and other properties Chen, Meng Wang, Xue-ping General Mathematics This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function with neutral element in $[0,\infty]$, $t: [0,1]\rightarrow [0,\infty]$ is a left continuous monotone function and $t^{[-1]}:[0,\infty]\rightarrow[0,1]$ is the weak pseudo-inverse of $t$. It shows that the associativity of the function $T$ depends only on properties of the range of $t$. Moreover, it investigates the idempotence, the limit property, the conditional cancellation law and the continuity of the function $T$, respectively. |
| title | Associativity of two-place functions generated by left continuous monotone functions and other properties |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2411.12744 |