| Title:
|
On reverses of some binary operators (English) |
| Author:
|
Šabo, Michal |
| Author:
|
Strežo, Peter |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
[435]-450 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated. (English) |
| Keyword:
|
reverse of binary operations |
| Keyword:
|
fuzzy preference structures |
| MSC:
|
03E72 |
| MSC:
|
08A72 |
| MSC:
|
39B05 |
| idZBL:
|
Zbl 1249.08010 |
| idMR:
|
MR2180356 |
| . |
| Date available:
|
2009-09-24T20:10:18Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135668 |
| . |
| Reference:
|
[1] Baets B. De, Fodor J.: Twenty years of fuzzy preference structures (1978 – 1997).Belg. J. Oper. Res. Statist. Comput. Sci. 37 (1997), 61–81 Zbl 0926.91012, MR 1619319 |
| Reference:
|
[2] Baets B. De, Fodor J.: Generator triplets of additive preference structures.Academia Press, Gent 2003, pp. 15–25 |
| Reference:
|
[3] Baets B. De, Mayer H. De: The Frank family in fuzzy similarity measurement.In: Proc. Eusflat, Leicester 2001, pp. 15–23 |
| Reference:
|
[4] Fodor J., Roubens M.: Fuzzy Preference Modeling and Multicriteria Decision Support.Kluwer Academic Publishers, Dordrecht 1994 |
| Reference:
|
[5] Fodor J., Jenei S.: On reversible triangular t-norms.Fuzzy Sets and Systems 104 (1999), 1, 43–51 MR 1685808 |
| Reference:
|
[6] Frank M. J.: On the simultaneous associativity of $F(x,y)$ and $x+y-F(x,y)$.Aequationes Math. 19 (1979), 194–226 Zbl 0444.39003, MR 0556722, 10.1007/BF02189866 |
| Reference:
|
[7] Jenei S.: Fibred triangular norms.Fuzzy Sets and Systems 103 (1999), 68–82 Zbl 0946.26017, MR 1674034 |
| Reference:
|
[8] Kimberling C.: On a class of associative function.Publ. Math. Debrecen 20 (1973), 21–39 MR 0333504 |
| Reference:
|
[9] Klement E. P., Mesiar, R., Pap E.: On some geometric tranformations of t-norms.Mathware & Soft Computing 5 (1998), 57–67 MR 1632763 |
| Reference:
|
[10] Klement E. P., Mesiar, R., Pap E.: Invariant copulas.Kybernetika 38 (2002), 275–285 MR 1944309 |
| Reference:
|
[11] Klement E. P., Mesiar, R., Pap E.: Measure-based aggregation operators.Fuzzy Sets and Systems 142 (2004), 3–14 Zbl 1046.28011, MR 2045339, 10.1016/j.fss.2003.10.028 |
| Reference:
|
[12] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
| Reference:
|
[13] Kolesárová A., Mordelová J.: 1-Lipschitz and kernel aggregation operators.In: Proc. Summmer School on Aggregation Operators and their Applications, Oviedo 2001, pp. 71–75 |
| Reference:
|
[14] Lazaro J., Rückschlossová, T., Calvo T.: Shift invariant binary aggregation operators.Fuzzy Sets and Systems 142 (2004), 51–62 Zbl 1081.68106, MR 2045342, 10.1016/j.fss.2003.10.031 |
| Reference:
|
[15] Mesiarová A.: Continuous triangular subnorms.Fuzzy Sets and Systems 142 (2004), 75–83 Zbl 1043.03018, MR 2045344 |
| Reference:
|
[16] Moyniham R.: On $\tau _{T}$ semigroups of probability distributions II.Aequationes Math. 17 (1978), 19–40 |
| Reference:
|
[17] Nelsen R. B.: An Introduction to Copulas.(Lecture Notes in Statistics 139.) Springer, New York 1999 Zbl 1152.62030, MR 1653203, 10.1007/978-1-4757-3076-0 |
| Reference:
|
[18] Šabo M.: On t-reverse of t-norms.Tatra Mt. Math. Publ. 12 (1997), 35–40 Zbl 0954.03060, MR 1607131 |
| Reference:
|
[19] Šabo M.: Fuzzy preference structures and t-reversible t-norm.Busefal 76 (1998), 29–33 |
| Reference:
|
[20] Schweizer B., Sklar A.: Probabilistic Metric Spaces.North–Holland, New York 1963 Zbl 0546.60010, MR 0790314 |
| Reference:
|
[21] Walle B. Van de, Baets, B. De, Kerre E. E.: A comparative study of completeness conditions in fuzzy preference structures.In: Proc. IFSA’97, Prague, Vol. III, pp. 74–79 |
| . |
