On Quasi-discrete Fuzzy Closure Spaces

Issue title: Rough Sets and Fuzzy Sets

Article type: Research Article

Authors: Liu, Guilong^{a; *}

Affiliations: [a] School of Information Science, Beijing Language and Culture University, Beijing 100083, China. [email protected]

Correspondence: [*] Address for correspondence: School of Information Science, Beijing Language and Culture University, Beijing 100083, China

Abstract: This paper studies quasi-discrete closure spaces and fuzzy closure spaces. We show that any topological closure cT induced by a closure c is the smallest extension from a closure space to a topological closure space in both crisp and fuzzy environment, in addition, a characterization of the continuous mappings in quasi-discrete closure spaces is obtained. We propose the concept of quasi-discrete fuzzy closure spaces in the context of fuzzy sets and establish a one to one correspondence between quasi-discrete fuzzy closure spaces and reflexive fuzzy relations. We also discuss the relationship between topological closure cT and closure c in quasi-discrete fuzzy closure spaces and show that the process from closure c to topological closure cT can be realized via the process from a reflexive fuzzy relation to its transitive closure.

Keywords: Fuzzy relation, Topology, Fuzzy topological closure, Quasi-discreteness, Fuzzy set

DOI: 10.3233/FI-2015-1286

Journal: Fundamenta Informaticae, vol. 142, no. 1-4, pp. 105-115, 2015