Geodesic
$T$-extension as a method of construction of a generalized aggregation operator
Kybernetika, Tome 46 (2010) no. 6, pp. 1078-1097 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03E72, 94D05
Keywords: aggregation operator; t-norm; $T$-extension 
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Lebedinska, Julija. $T$-extension as a method of construction of a generalized aggregation operator. Kybernetika, Tome 46 (2010) no. 6, pp. 1078-1097. http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a12/

[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. | MR | Zbl

[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

[3] Grabisch, M., Marichal, J-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York 2009. | MR | Zbl

[4] Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Series: Trends in Logic, Vol. 8. Kluwer Academic Publishers, Dordrecth 2000. | MR | Zbl

[5] Kruse, R., Gebhardt, J., Klawon, F.: Foundations of Fuzzy Systems. John Wiley and Sons, Chichester, New York, Birsbane, Toronto, Singapore 1998.

[6] Lebedinska, J.: $\gamma $-aggregation operators and some aspects of generalized aggregation problem. Math. Model. Anal. 15 (2010), 1, 83–96. | DOI | MR | Zbl

[7] Lebedinska, J.: Fuzzy Matrices and Generalized Aggregation Operators: Theoretical Foundations and Possible Applications. PhD. Theses, University of Latvia, Riga 2010.

[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.

[9] Rudas, I. J., Fodor, J.: Information Aggregation in Intelligent Systems Using Generalized Operators. Internat. J. Computers, Communications and Control 1 (2006),1, 47–57.

[10] Šostaks, A.: $L$-kopas un $L$-vērtīgas struktūras (in Latvian). Latvijas Universitāte, Mācību grāmata, Rīga 2003.

[11] Takači, A.: General aggregation operators acting on fuzzy numbers induced by ordinary aggregation operators. Novi Sad J. Math. 33 (2003), 2, 67–76. | MR | Zbl

[12] Yager, R.: Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making 3 (2004), 1, 93–107. | DOI | MR | Zbl