Characterizations of monotone right continuous functions which generate associative functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909881392431104 |
|---|---|
| author | Zhang, Yun-Mao Wang, Xue-ping |
| author_facet | Zhang, Yun-Mao Wang, Xue-ping |
| contents | Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ where $T^*:[0,1]^2\rightarrow[0,1]$ is an associative function with neutral element in $[0,1]$, $f: [0,1]\rightarrow [0,1]$ is a monotone right continuous function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ is the pseudo-inverse of $f$ depends only on properties of the range of $f$. The necessary and sufficient conditions for the $T$ to be associative are presented by applying the properties of the monotone right continuous function $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizations of monotone right continuous functions which generate associative functions Zhang, Yun-Mao Wang, Xue-ping Functional Analysis Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ where $T^*:[0,1]^2\rightarrow[0,1]$ is an associative function with neutral element in $[0,1]$, $f: [0,1]\rightarrow [0,1]$ is a monotone right continuous function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ is the pseudo-inverse of $f$ depends only on properties of the range of $f$. The necessary and sufficient conditions for the $T$ to be associative are presented by applying the properties of the monotone right continuous function $f$. |
| title | Characterizations of monotone right continuous functions which generate associative functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.18944 |