On quasi-discrete fuzzy closure spaces (Q2823244)

The author studies quasi-discrete closure spaces and fuzzy closure spaces. He shows that any topological closure \(c_T\) induced by a closure \(c\) is the smallest extension from a closure space to a topological closure space in both the crisp and the fuzzy environment. In addition, he gives a characterization of a continuous mapping between two quasi-discrete closure spaces. He proposes the concept of a quasi-discrete fuzzy closure space in the context of fuzzy sets and establishes a one-to-one correspondence between quasi-discrete fuzzy closure spaces and reflexive fuzzy relations. He also discusses the relationship between topological closure \(c_T\) and \(c\) in a quasi-discrete fuzzy closure space and shows that the process from closure to topological closure can be realized via the process from a reflexive fuzzy relation to its transitive closure.