The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures
type: Item
instance of: scholarly article
title: The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures
zbMATH Open document ID: 0685.54007
DOI: 10.1016/0165-0114(89)90067-5
author: Proper Maes
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 4122805
zbMATH Keywords: fuzzy uniform space
zbMATH Keywords: fuzzy neighborhood space
zbMATH Keywords: Hausdorff-Bourbaki fuzzy uniformity
zbMATH Keywords: semi-Vietoris fuzzy neighborhood structures
zbMATH Keywords: Weiss precompact fuzzy sets
zbMATH Keywords: Weiss-compact fuzzy sets
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90067-5
OpenAlex ID: W2058934120
cites work: On Quasi-Uniformities in Hyperspaces
cites work: Compact supported endographs and fuzzy sets
cites work: Q5541832
cites work: Q3304890
cites work: Fuzzy uniform spaces
cites work: Fuzzy neighborhood spaces
cites work: Hyperspaces of fuzzy sets
cites work: Completeness properties of hyperspaces of compact fuzzy sets
cites work: Topologies on Spaces of Subsets
cites work: Fuzzy sets
description: scientific article; zbMATH DE number 4122805