| Title:
|
Generated fuzzy implications and fuzzy preference structures (English) |
| Author:
|
Biba, Vladislav |
| Author:
|
Hliněná, Dana |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
453-464 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet $(p,i,j)$, which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated. (English) |
| Keyword:
|
generated fuzzy implication |
| Keyword:
|
fuzzy preference structure |
| Keyword:
|
fuzzy implications |
| Keyword:
|
t-norm |
| MSC:
|
08A72 |
| MSC:
|
28E10 |
| MSC:
|
60A05 |
| idMR:
|
MR2975800 |
| . |
| Date available:
|
2012-08-31T15:54:31Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142948 |
| . |
| Reference:
|
[1] Alsina, C.: On a family of connectives for fuzzy sets.Fuzzy Sets and Systems 16 (1985), 231–235. Zbl 0603.39005, MR 0801264, 10.1016/0165-0114(85)90026-0 |
| Reference:
|
[2] Baczyński, M., Jayaram, B.: Fuzzy implications (Studies in Fuzziness and Soft Computing, Vol. 231).Springer, Berlin 2008. |
| Reference:
|
[3] Fodor, J. C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support.Kluwer Academic Publishers, Dordrecht 1994. Zbl 0827.90002, MR 1672363 |
| Reference:
|
[4] Hliněná, D., Biba, V.: Generated fuzzy implications and known classes of implications.In: Acta Universitatis Matthiae Belii ser. Mathematics. 1., Matej Bel University, Banská Bystrica 2010, pp. 25–34. Zbl 1205.03035, MR 2771563 |
| Reference:
|
[5] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms.Kluwer, Dordrecht 2000. Zbl 1087.20041, MR 1790096 |
| Reference:
|
[6] Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions.IEEE Trans. Fuzzy Systems 15 (2007), 6, 1107–1121. 10.1109/TFUZZ.2007.896304 |
| Reference:
|
[7] Smutná, D.: On many valued conjunctions and implications.J. Electr. Engrg. 50 (1999), 10/s, 8–10. |
| Reference:
|
[8] Van De Walle, B., De Baets, B., Kerre, E.: A comparative study of completeness conditions in fuzzy preference structures.In: Proc. IFSA'97, vol. III, Prague, pp. 74–79. |
| Reference:
|
[9] Zadeh, L. A.: Similarity relations and fuzzy orderings.Inform. Sci. 3 (1971), 177–200. Zbl 0218.02058, MR 0297650, 10.1016/S0020-0255(71)80005-1 |
| . |
