On embedding problem of fuzzy number valued continuous functions

Article type: Research Article

Authors: Aygünoğlu, Abdülkadir | Çetkin, Vildan | Aygün, Halis

Affiliations: Department of Mathematics, University of Kocaeli, Umuttepe Campus, Kocaeli, Turkey

Note: [] Corresponding author. Halis Aygün, Department of Mathematics, University of Kocaeli, Umuttepe Campus, 41380 Kocaeli, Turkey. E-mails: [email protected] (Halis Aygün); [email protected] (Abdülkadir Aygünoğlu); [email protected] (Vildan Çetkin).

Abstract: In this paper, we show that the complete metric space C(K,$\mathbb{E}^{1}$) of fuzzy number valued continuous functions on a compact set K can be embedded into a Banach space C(K × [0,1]) × C(K × [0,1]) isometrically and isomorphically.

Keywords: Fuzzy number space, fuzzy number valued function, embedding, isometrical isomorphism

DOI: 10.3233/IFS-2012-0631

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 1, pp. 243-246, 2013