Title of paper:

Taylor's theorem for functions, defined on Atanassov IFsets

Author(s):

Alžbeta Michalíková

Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK974 01 Banská Bystrica, Slovakia

Alzbeta.Michalikovaumb.sk


Presented at:

17th International Conference on Intuitionistic Fuzzy Sets, 1–2 November 2013, Sofia, Bulgaria

Published in:

"Notes on IFS", Volume 19, 2013, Number 3, pages 34—41

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Abstract:

IFsets were first time defined in the paper [1] and they represent the natural extension of the theory of fuzzy sets. In the paper [6] there was proved that Lagrange theorem holds for functions defined on IFsets. Therefore it is natural question if it is possible to prove also Taylor’s theorem for functions defined on IFsets. To prove this theorem we defined polynomial function and Taylor’s formula for functions defined on IFsets. Then the Taylor’s theorem is proved.

Keywords:

IFset, Polynomial function, Taylor’s formula, Taylor’s theorem.

AMS Classification:

03E72

References:

 Atanassov, K. Intuitionistic Fuzzy Sets. Springer, Berlin, 1999.
 Atanassov, K., B. Riečan. On two operations over intuitionistic fuzzy sets. Journal of Applied Mathematics, Statistics and Informatics, Vol. 2, 2006, No. 2, 145–148.
 Hollá, I., B. Riečan. Elementary function on IF sets. Issues in Soft Computing. Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2008, 193–201.
 Michalíková, A. The differential calculus on IF sets. FUZZIEEE 2009. International Conference on Fuzzy Systems. Proccedings [CDROM]. Jeju Island, Korea, 2009, 1393–1395.
 Michalíková, A. Some notes about boundaries on IF sets. New Trends in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized nets and Related Topics. Volume I: Foundations. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland, 2013, 105–113.
 Riečan, B. On Lagrange mean value theorem for functions on Atanassov IFsets. Proceedings of the Eighth International Workshop on Intuitionistic Fuzzy Sets. October 9, 2012, Banská Bystrica, Slovakia. Notes on Intuitionistic Fuzzy Sets, Vol. 18, 2012, No. 4, 8–11.

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