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On Quasi-discrete Fuzzy Closure Spaces

Liu G.

Fundamenta Informaticae

2015

Vol. 142, nr 1-4

105--115

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.