| Title:
|
Smooth implications on a finite chain (English) |
| Author:
|
Su, Yong |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
668-674 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized. (English) |
| Keyword:
|
implications |
| Keyword:
|
finite chain |
| Keyword:
|
smoothness |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| idZBL:
|
Zbl 07177909 |
| idMR:
|
MR4043541 |
| DOI:
|
10.14736/kyb-2019-4-0668 |
| . |
| Date available:
|
2020-01-10T14:21:51Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147962 |
| . |
| Reference:
|
[1] Baczyński, M., Jayaram, B.: Fuzzy Implications..In: Studies in Fuzziness and Soft Computing, Vol. 231, Springer, Berlin 2008. Zbl 1293.03012, MR 2428086 |
| Reference:
|
[2] Fodor, J.: Smooth associative operations on finite ordinal scales..IEEE Trans. Fuzzy Systems 8 (2000), 6, 791-795. 10.1109/91.890343 |
| Reference:
|
[3] Mas, M., Monserrat, M., Torrens, J.: S-implications and R-implications on a finite chain..Kybernetika 40 (2004), 1, 3-20. MR 2068595 |
| Reference:
|
[4] Mas, M., Monserrat, M., Torrens, J.: On two types of discrete implications..Int. J. Approx. Reason. 40 (2005), 262-279. MR 2193766, 10.1016/j.ijar.2005.05.001 |
| Reference:
|
[5] Mayor, G., Torrens, J.: On a class of operators for expert systems..Int. J. Intell. Systems 8 (1993), 771-778. Zbl 0785.68087, 10.1002/int.4550080703 |
| Reference:
|
[6] Shi, Y., Gasse, B. Van, Ruan, D., Kerre, E. E.: On dependencies and independencies of fuzzy implication axioms..Fuzzy Sets and Systems 161 (2010), 1388-1405. MR 2606421, 10.1016/j.fss.2009.12.003 |
| Reference:
|
[7] Yager, R. R.: Non-numeric multi-criteria multi-person decision making..Group Decisions Negotiation 2 (1993), 81-93. 10.1007/bf01384404 |
| . |
