Alexandrov L-preuniform convergence structures

Article type: Research Article

Authors: Davvaz, Bijan^{a; b} | Kim, Yong Chan^{a; b; *}

Affiliations: [a] Department of Mathematics, Yazd University, Yazd, Iran | [b] Department of Mathematics, Gangneung-Wonju National University, Gangneung, Korea

Correspondence: [*] Corresponding author. Yong Chan Kim. Tel.: 82 33 640 2270; Fax: 82 33 647 3256; E-mail: [email protected].

Abstract: In this paper, we introduce the notion of Alexandrov L-preuniform convergence spaces based on the concepts of Alexandrov L-filters on X × X. We investigate the categorical relations among Alexandrov L-preuniform convergence spaces, Alexandrov L-preconvergence spaces and reflexive L-fuzzy relations. Moreover, we investigate their topological properties and give their examples as a viewpoint of the topological structure for fuzzy information and fuzzy rough sets.

Keywords: Complete residuated lattices, fuzzy join(meet)-complete lattices, L-fuzzy preordered sets, Alexandrov L-(neighborhood) filters, Alexandrov L-preuniform convergence spaces, Alexandrov L-preconvergence spaces

DOI: 10.3233/JIFS-181892

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3697-3709, 2019