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On Fourier Series of Fuzzy-Valued Functions
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-10
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering.
In the present paper since the utilization of Zadeh’s Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function.
We derive uniform convergence of a fuzzy-valued function sequences and series with level sets.
Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions.
Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example.
Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.
American Psychological Association (APA)
Kadak, Uğur& Başar, Feyzi. 2014. On Fourier Series of Fuzzy-Valued Functions. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1051006
Modern Language Association (MLA)
Kadak, Uğur& Başar, Feyzi. On Fourier Series of Fuzzy-Valued Functions. The Scientific World Journal No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1051006
American Medical Association (AMA)
Kadak, Uğur& Başar, Feyzi. On Fourier Series of Fuzzy-Valued Functions. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1051006
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1051006