The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures
The Hausdorff-Bourbaki fuzzy uniformity [\textit{R. Lowen}, Fuzzy Sets Syst. 9, 278-311 (1983; Zbl 0546.54010)] is shown to be the supremum of the upper and lower fuzzy quasi-uniformities. The relations of these structures with the semi-Vietoris fuzzy neighborhood structures are studied. For example, on the Weiss precompact fuzzy sets the Vietoris fuzzy neighborhood system is finer than that derived from the Hausdorff- Bourbaki structure with equality holding on the Weiss-compact fuzzy sets.
semi-Vietoris fuzzy neighborhood structures
scientific article; zbMATH DE number 4122805