T -extension as a method of construction of a generalized aggregation operator

Julija Lebedinska

Kybernetika (2010)

  • Volume: 46, Issue: 6, page 1078-1097
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Lebedinska, Julija. "$T$-extension as a method of construction of a generalized aggregation operator." Kybernetika 46.6 (2010): 1078-1097. <http://eudml.org/doc/196727>.

@article{Lebedinska2010,
abstract = {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.},
author = {Lebedinska, Julija},
journal = {Kybernetika},
keywords = {aggregation operator; t-norm; $T$-extension; aggregation operator; t-norm; -extension},
language = {eng},
number = {6},
pages = {1078-1097},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$T$-extension as a method of construction of a generalized aggregation operator},
url = {http://eudml.org/doc/196727},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Lebedinska, Julija
TI - $T$-extension as a method of construction of a generalized aggregation operator
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 6
SP - 1078
EP - 1097
AB - 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.
LA - eng
KW - aggregation operator; t-norm; $T$-extension; aggregation operator; t-norm; -extension
UR - http://eudml.org/doc/196727
ER -

References

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  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. (2002) Zbl1039.03015MR1936384
  2. Dubois, D., Ostasiewicz, W., H.Prade, Fuzzy Sets: History and Basic Notions: Fundamentals of Fuzzy Sets, Kluwer Academic Publ., Boston, Dodrecht, London 1999. (1999) MR1890230
  3. Grabisch, M., Marichal, J-L., Mesiar, R., Pap, E., Aggregation Functions, Cambridge University Press, New York 2009. (2009) Zbl1196.00002MR2538324
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  5. Kruse, R., Gebhardt, J., Klawon, F., Foundations of Fuzzy Systems, John Wiley and Sons, Chichester, New York, Birsbane, Toronto, Singapore 1998. (1998) 
  6. Lebedinska, J., 10.3846/1392-6292.2010.15.83-96, Math. Model. Anal. 15 (2010), 1, 83–96. (2010) Zbl1203.03083MR2641928DOI10.3846/1392-6292.2010.15.83-96
  7. Lebedinska, J., Fuzzy Matrices and Generalized Aggregation Operators: Theoretical Foundations and Possible Applications, PhD. Theses, University of Latvia, Riga 2010. (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. (2009) 
  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. (2006) 
  10. Šostaks, A., L -kopas un L -vērtīgas struktūras (in Latvian), Latvijas Universitāte, Mācību grāmata, Rīga 2003. (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. (2003) Zbl1202.03061MR2046163
  12. Yager, R., 10.1023/B:FODM.0000013074.68765.97, Fuzzy Optimization and Decision Making 3 (2004), 1, 93–107. (2004) Zbl1057.90032MR2047106DOI10.1023/B:FODM.0000013074.68765.97

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