The comparative study of gradual and fuzzy normed linear spaces

Article type: Research Article

Authors: Sadeqi, Ildar^* | Azari, Farnaz Yaqub

Affiliations: Department of Mathematics, Sahand University of Technology, Tabriz, Iran

Correspondence: [*] Corresponding author. Ildar Sadeqi, Department of Mathematics,Sahand University of Technology, Tabriz, Iran. Tel.: +98 413 345 9054; Fax: +98 413 344 4430; E-mail: [email protected].

Abstract: In this paper, a comparative study of two types of norms on a linear space, namely gradual norm and fuzzy norm has been made and it is shown that they are equivalent in general. Because a gradual normed linear space is a locally convex space so a fuzzy normed linear space is also a locally convex space in classical sense. Therefore, most of results in classical locally convex spaces do hold in fuzzy normed linear spaces.

Keywords: Gradual number, gradual norm, fuzzy interval, fuzzy norm, locally convex space

DOI: 10.3233/IFS-151843

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1195-1198, 2016