Distance functions, upper approximation operators and Alexandrov fuzzy topologies

Article type: Research Article

Authors: Oh, Ju-Mok | 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 25457, Korea. E-mail: yck@gwnu.ac.kr.

Abstract: In this paper, we introduce the notions of join preserving maps using distance spaces instead of fuzzy partially ordered sets on complete co-residuated lattices. We investigate the properties of Alexandrov fuzzy topologies, distance functions, join preserving maps and upper approximation operators. Furthermore, we study their relations and examples. We prove that there exist isomorphic categories and Galois correspondences between their categories.

Keywords: Complete co-residuated lattices, distance functions, join preserving maps, upper approximation operators, Alexandrov fuzzy topologies

DOI: 10.3233/JIFS-210061

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 11927-11939, 2021