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Title of paper:

Kurzweil–Henstock integral for IFfunctions

Author(s):

Jaroslav Považan

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

jaroslav.povazanumb.sk


Published in:

"Notes on IFS", Volume 23, 2017, Number 3, pages 30—43

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PDF (157 Kb Kb, Info)

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 IFnumbers. In this contribution we are going to extend the definitions and the results for functions which has IFnumbers as their values.

Keywords:

Kurzweil–Henstock integral, fuzzy numbers, fuzzy functions, IFnumbers, IFfunctions, δ  fine division of interval.

AMS Classification:

03E72

References:

 Henstock, R. (1963) Theory of Integration. Butterworths, London.
 Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Springer Physica Verlag, Heidelberg.
 Kluvancová, D., & Riečan, B. (2016) On IFnumbers. Notes on Intuitionistic Fuzzy Sets, 22(3), 9–14.
 Kurzweil, J. (1957) Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J., 7(82), 418–446.
 Uzzal Asfan, B., M. On convergence theorems for fuzzy Henstock integrals. Iranian Journal of Fuzzy Systems. (to appear)

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