| Title:
|
Yager’s classes of fuzzy implications: some properties and intersections (English) |
| Author:
|
Baczyński, Michał |
| Author:
|
Jayaram, Balasubramaniam |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
157-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager_2004] has introduced two new classes of fuzzy implications called the $f$-generated and $g$-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$-generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst themselves and with the well established $(S,N)$-implications and $R$-implications. In the cases where they intersect the precise sub-families have been determined. (English) |
| Keyword:
|
fuzzy implication |
| Keyword:
|
$f$-generated implication |
| Keyword:
|
$g$-generated implication |
| Keyword:
|
$h$-generated implication |
| Keyword:
|
$(S;N)$-implication |
| Keyword:
|
$S$-implication |
| Keyword:
|
$R$-implication |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| MSC:
|
39B99 |
| idZBL:
|
Zbl 1132.03330 |
| idMR:
|
MR2343393 |
| . |
| Date available:
|
2009-09-24T20:22:37Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135764 |
| . |
| Reference:
|
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| Reference:
|
[2] Balasubramaniam J.: Contrapositive symmetrization of fuzzy implications – Revisited.Fuzzy Sets and Systems 157 (2006), 2291–2310 MR 2251837 |
| Reference:
|
[3] Balasubramaniam J.: Yager’s new class of implications $J_f$ and some classical tautologies.Inform. Sci. 177 (2007), 930–946 Zbl 1142.68539, MR 2288674 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Trillas E., Valverde L.: On some functionally expressable implications for fuzzy set theory.In: Proc. 3rd Internat. Seminar on Fuzzy Set Theory (E. P. Klement, ed.), Johannes Kepler Universität, Linz 1981, pp. 173–190 Zbl 0498.03015, MR 0646807 |
| Reference:
|
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| Reference:
|
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| . |
