| Title:
|
Homogeneous aggregation operators (English) |
| Author:
|
Rückschlossová, Tatiana |
| Author:
|
Rückschloss, Roman |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
279-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance of aggregation operators. Several examples are included. (English) |
| Keyword:
|
aggregation operator |
| Keyword:
|
homogeneity |
| Keyword:
|
kernel property |
| MSC:
|
03E72 |
| MSC:
|
26B99 |
| MSC:
|
68T37 |
| idZBL:
|
Zbl 1249.26024 |
| idMR:
|
MR2253389 |
| . |
| Date available:
|
2009-09-24T20:15:52Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135714 |
| . |
| Reference:
|
[1] Aczél J., Gronau, D., Schwaiger J.: Increasing solutions of the homogeneity equation and similar equations.J. Math. Anal. Appl. 182 (1994), 436–464 MR 1269471, 10.1006/jmaa.1994.1097 |
| Reference:
|
[2] Calvo T., Mesiar R.: Stability of aggregation operators.In: Proc. EUSFLAT’2001, Leicester 2001, pp. 475–478 MR 1821982 |
| Reference:
|
[3] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: Basic concepts, issues and properties.In: Aggregation Operators. New Trends and Applications (T. Calvo, G. Mayor, and R. Mesiar, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–105 MR 1936383 |
| Reference:
|
[4] Calvo T., Mesiar, R., Yager R. R.: Quantitative weights and aggregation.IEEE Trans. Fuzzy Systems 12 (2004), 1, 62–69 MR 2073568, 10.1109/TFUZZ.2003.822679 |
| Reference:
|
[5] Dujmovic J. J.: Weighted conjuctive and disjunctive means and their application in system evaluation.Univ. Beograd Publ. Elektrotehn. Fak. 483 (1974), 147–158 MR 0378884 |
| Reference:
|
[6] Grabisch M.: Symmetric and asymmetric integrals: the ordinal case.In: Proc. IIZUKA’2000, Iizuka 2000, CD-rom |
| Reference:
|
[7] Grabisch M., Murofushi, T., Sugeno M., (eds.) M.: Fuzzy Measures and Integrals.Theory and Applications. Physica–Verlag, Heidelberg 2000 Zbl 0935.00014, MR 1767776 |
| Reference:
|
[8] Klir G. J., Folger T. A.: Fuzzy Sets, Uncertainty, and Information.Prentice Hall, Englewood Cliffs, New Jersey 1988 Zbl 0675.94025, MR 0930102 |
| Reference:
|
[9] Kolesárová A., Mordelová J.: 1-Lipschitz and kernel aggregation operators.In: Proc. AGOP’2001, Oviedo 2001, pp. 71–75 |
| Reference:
|
[10] Lázaro 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:
|
[11] Mesiar R., Rückschlossová T.: Characterization of invariant aggregation operators.Fuzzy Sets and Systems 142 (2004), 63–73 Zbl 1049.68133, MR 2045343, 10.1016/j.fss.2003.10.032 |
| Reference:
|
[12] Nagumo M.: Über eine Klasse der Mittelwerte.Japan. J. Math. 7 (1930), 71–79 |
| Reference:
|
[13] Rückschlossová T.: Aggregation Operators and Invariantness.Ph.D. Thesis, Slovak University of Technology, Bratislava 2004 |
| Reference:
|
[14] Zadeh L. A.: Fuzzy sets.Inform. and Control 8 (1965), 338–353 Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
| . |
