| Title of paper:
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Taylor's theorem for functions, defined on Atanassov IF-sets
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| Author(s):
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| Alžbeta Michalíková
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| Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia
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| Alzbeta.Michalikova@umb.sk
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| Presented at:
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17th International Conference on Intuitionistic Fuzzy Sets, 1–2 November 2013, Sofia, Bulgaria
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| Published in:
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"Notes on IFS", Volume 19, 2013, Number 3, pages 34—41
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| Download:
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 PDF (156 Kb, File info)
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| Abstract:
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IF-sets 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 IF-sets. Therefore it is natural question if it is possible to prove also Taylor’s theorem for functions defined on IF-sets. To prove this theorem we defined polynomial function and Taylor’s formula for functions defined on IF-sets. Then the Taylor’s theorem is proved.
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| Keywords:
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IF-set, Polynomial function, Taylor’s formula, Taylor’s theorem.
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| AMS Classification:
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03E72
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| References:
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- 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. FUZZ-IEEE 2009. International Conference on Fuzzy Systems. Proccedings [CD-ROM]. 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 IF-sets. 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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