| Title:
|
$T$-extension as a method of construction of a generalized aggregation operator (English) |
| Author:
|
Lebedinska, Julija |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
6 |
| Year:
|
2010 |
| Pages:
|
1078-1097 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Generalized aggregation operators are the tool for aggregation of fuzzy sets. The apparatus was introduced by Takači in [11]. $T$-extension is a construction method of a generalized aggregation operator and we study it in the paper. We observe the behavior of a $T$-extension with respect to different order relations and we investigate properties of the construction. (English) |
| Keyword:
|
aggregation operator |
| Keyword:
|
t-norm |
| Keyword:
|
$T$-extension |
| MSC:
|
03E72 |
| MSC:
|
94D05 |
| idZBL:
|
Zbl 1225.94033 |
| idMR:
|
MR2797429 |
| . |
| Date available:
|
2011-04-12T12:53:42Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141468 |
| . |
| Reference:
|
[1] Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation Operators: Properties, Classes and Construction methods.In: Aggregation Operators: New Trends and Applications. Studies in Fuzziness and Soft Computing (T.Calvo, G. Mayor, and R.Mesiar, eds.), Physica – Verlag, New York 2002, pp. 3–104. Zbl 1039.03015, MR 1936384 |
| Reference:
|
[2] Dubois, D., Ostasiewicz, W., H.Prade: Fuzzy Sets: History and Basic Notions: Fundamentals of Fuzzy Sets.Kluwer Academic Publ., Boston, Dodrecht, London 1999. MR 1890230 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Kruse, R., Gebhardt, J., Klawon, F.: Foundations of Fuzzy Systems.John Wiley and Sons, Chichester, New York, Birsbane, Toronto, Singapore 1998. |
| Reference:
|
[6] Lebedinska, J.: $\gamma $-aggregation operators and some aspects of generalized aggregation problem.Math. Model. Anal. 15 (2010), 1, 83–96. Zbl 1203.03083, MR 2641928, 10.3846/1392-6292.2010.15.83-96 |
| Reference:
|
[7] Lebedinska, J.: Fuzzy Matrices and Generalized Aggregation Operators: Theoretical Foundations and Possible Applications.PhD. Theses, University of Latvia, Riga 2010. |
| Reference:
|
[8] Merigo, J. M., Ramon, M. C.: The induced generalized hybrid averaging operator and its application in financial decision making.Internat. J. of Business, Economics, Finance and Management Sciences 1 (2009), 2, 95–101. |
| Reference:
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| Reference:
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[10] Šostaks, A.: $L$-kopas un $L$-vērtīgas struktūras (in Latvian).Latvijas Universitāte, Mācību grāmata, Rīga 2003. |
| Reference:
|
[11] Takači, A.: General aggregation operators acting on fuzzy numbers induced by ordinary aggregation operators.Novi Sad J. Math. 33 (2003), 2, 67–76. Zbl 1202.03061, MR 2046163 |
| Reference:
|
[12] Yager, R.: Generalized OWA aggregation operators.Fuzzy Optimization and Decision Making 3 (2004), 1, 93–107. Zbl 1057.90032, MR 2047106, 10.1023/B:FODM.0000013074.68765.97 |
| . |
