title: On Fourier series of fuzzy-valued functions.
abstract: 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.
authors: Department of Mathematics, Faculty of Science, Bozok University, Yozgat, Turkey ; Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey.
authors: Uğur
authors: 0000-0001-7095-5257
authors: U
authors: Kadak
authors: Department of Mathematics, Faculty of Arts and Sciences, Fatih University, 34500 İstanbul, Turkey.
authors: Feyzi
authors: F
authors: Başar
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D017143:Fuzzy Logic; D008433:Mathematics / Q000379:methods*; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted