L-fuzzy N-convergence structures

Article type: Research Article

Authors: Pang, Bin^{a; b} | Zhao, Yi^{a; *}

Affiliations: [a] Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P.R. China | [b] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Yi Zhao, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, P.R. China. E-mail: zhyky@msn.com.

Abstract: Based on a completely distributive lattice L, the concept of L-fuzzy N-convergence structures is introduced. It is shown that the category of L-fuzzy topological spaces can be embedded in the category of L-fuzzy N-convergence spaces. It is also proved the category of (topological) pretopological L-fuzzy N-convergence spaces is isomorphic to the category of (topological) L-fuzzy neighborhood spaces and the former is a bireflective subcategory of the category of L-fuzzy N-convergence spaces.

Keywords: L-fuzzy topology, L-fuzzy N-convergence structure, L-filter, category theory, L-fuzzy neighborhood system

DOI: 10.3233/IFS-152021

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 5, pp. 3033-3043, 2016