The relationships between L-fuzzy topogenous orders and topological structures

Article type: Research Article

Authors: Oh, Ju-Mok | Kim, Yong Chan^{; *; 1}

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 210-702, Korea. E-mail: [email protected].

Note: [1] This work was supported by Research Fund of Gangneung-Wonju National University in 2016.

Abstract: In this paper, we introduce the notions of L-fuzzy topogenous orders, L-fuzzy topology, L-interior operators and L-closure operators in complete residuated lattices. Moreover, we investigate the relations among L-fuzzy topogenous orders, L-interior operators and L-closure operators. We show that there is a Galois correspondence between the category of separated L-fuzzy interior (resp. closure) spaces and that of separated L-fuzzy topogenous (resp. cotopogenous) spaces.

Keywords: Complete residuated lattice, L-fuzzy topogenous orders, L-interior operators, L-closure operators, L-fuzzy topologies, Galois correspondence

DOI: 10.3233/JIFS-161267

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 4, pp. 2019-2032, 2017