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
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
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  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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