| Title:
|
S-implications and $R$-implications on a finite chain (English) |
| Author:
|
Mas, Margarita |
| Author:
|
Monserrat, Miquel |
| Author:
|
Torrens, Joan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
[3]-20 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is devoted to the study of two kinds of implications on a finite chain $L$: $S$-implications and $R$-implications. A characterization of each kind of these operators is given and a lot of different implications on $L$ are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class satisfies that both, its $S$-implication and its $R$-implication, agree. (English) |
| Keyword:
|
t-norm |
| Keyword:
|
T-conorm |
| Keyword:
|
finite chain |
| Keyword:
|
smoothness |
| Keyword:
|
implication operator |
| MSC:
|
03B52 |
| MSC:
|
06F05 |
| MSC:
|
94D05 |
| idZBL:
|
Zbl 1249.94094 |
| idMR:
|
MR2068595 |
| . |
| Date available:
|
2009-09-24T19:59:02Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135575 |
| . |
| Reference:
|
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