Alexandrov L-filters and Alexandrov L-convergence spaces¹

Article type: Research Article

Authors: Ko, Jung Mi | Kim, Yong Chan^{; *}

Affiliations: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea

Correspondence: [*] Corresponding author. Yong Chan Kim, Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea. E-mail: yck@gwnu.ac.kr.

Note: [1] This study was supported by Gangneung-Wonju National University.

Abstract: In this paper, we introduce the notion of Alexandrov L-(neighborhood) filters and Alexandrov L-convergence structures as a topological viewpoint of fuzzy rough sets. We investigate the categorical relations among Alexandrov L-neighborhood filters, L-fuzzy preorders and Alexandrov L-convergence structures. Moreover, we investigate their topological properties and give examples.

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

DOI: 10.3233/JIFS-171723

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 3, pp. 3255-3266, 2018