On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions. (4th October 2015)

• Record Type: Journal Article
• Authors: Kadak, Uğur; Efe, Hakan
• Other Names: Işik Mahmut Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-10-04
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/870179
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. 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 for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of H-differentiation and radius of convergence we examine the relationship between term by term H-differentiation and uniform convergence of fuzzy-valued function series.