8-9 October 2020 • Burgas, Bulgaria

Submission: 15 May 2020 • Notification: 31 May 2020 • Final Version: 15 June 2020

Issue:Kurzweil–Henstock integral for IF-functions

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http://ifigenia.org/wiki/issue:nifs/23/3/30-43
Title of paper: Kurzweil–Henstock integral for IF-functions
Author(s):
Jaroslav Považan
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
jaroslav.povazanAt sign.pngumb.sk
Published in: "Notes on IFS", Volume 23, 2017, Number 3, pages 30—43
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Abstract: TIn [1] and [3] there was presented a new definition for the definite integral for real functions based on Riemann’s sums with variable length of intervals in divisions. In [4] this definition was extended to functions with fuzzy values. In [2] there was introduced a notion of IF-numbers. In this contribution we are going to extend the definitions and the results for functions which has IF-numbers as their values.
Keywords: Kurzweil–Henstock integral, fuzzy numbers, fuzzy functions, IF-numbers, IF-functions, δ - fine division of interval.
AMS Classification: 03E72
References:
  1. Henstock, R. (1963) Theory of Integration. Butterworths, London.
  2. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Springer Physica Verlag, Heidelberg.
  3. Kluvancová, D., & Riečan, B. (2016) On IF-numbers. Notes on Intuitionistic Fuzzy Sets, 22(3), 9–14.
  4. Kurzweil, J. (1957) Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J., 7(82), 418–446.
  5. Uzzal Asfan, B., M. On convergence theorems for fuzzy Henstock integrals. Iranian Journal of Fuzzy Systems. (to appear)
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