16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019

Issue:Taylor's theorem for functions, defined on Atanassov IF-sets

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Title of paper: Taylor's theorem for functions, defined on Atanassov IF-sets
Author(s):
Alžbeta Michalíková
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia
Alzbeta.MichalikovaAt sign.pngumb.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: 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.
Keywords: IF-set, Polynomial function, Taylor’s formula, Taylor’s theorem.
AMS Classification: 03E72
References:
  1. Atanassov, K. Intuitionistic Fuzzy Sets. Springer, Berlin, 1999.
  2. 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.
  3. Hollá, I., B. Riečan. Elementary function on IF sets. Issues in Soft Computing. Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2008, 193–201.
  4. 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.
  5. 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.
  6. 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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