| Title:
|
New results on additive generator pairs of overlap and grouping functions (English) |
| Author:
|
Li-zhi, Liang |
| Author:
|
Xue-ping, Wang |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
238-263 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we deeply reveal the relationship between functions $\theta$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($\theta$,$\vartheta$), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $\theta$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions. (English) |
| Keyword:
|
overlap function |
| Keyword:
|
grouping function |
| Keyword:
|
triangular norm |
| Keyword:
|
additive generator pair |
| Keyword:
|
distortion |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| DOI:
|
10.14736/kyb-2025-2-0238 |
| . |
| Date available:
|
2025-06-02T09:55:20Z |
| Last updated:
|
2025-06-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152990 |
| . |
| Reference:
|
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| . |
