Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
aggregation operator; t-norm; $T$-extension
aggregation operator; t-norm; $T$-extension
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.
References:
[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 1936384 | Zbl 1039.03015
[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
[3] Grabisch, M., Marichal, J-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York 2009. MR 2538324 | Zbl 1196.00002
[4] Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Series: Trends in Logic, Vol. 8. Kluwer Academic Publishers, Dordrecth 2000. MR 1790096 | Zbl 1010.03046
[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 10.3846/1392-6292.2010.15.83-96 | MR 2641928 | Zbl 1203.03083
[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 2046163 | Zbl 1202.03061
[12] Yager, R.: Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making 3 (2004), 1, 93–107. DOI 10.1023/B:FODM.0000013074.68765.97 | MR 2047106 | Zbl 1057.90032
Search
Partner of
