Fuzzy filters
type: Item
instance of: scholarly article
title: Fuzzy filters
zbMATH Open document ID: 0647.54004
DOI: 10.1016/0022-247X(88)90271-5
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let X be a set and I the unit interval. In fuzzy topology, subsets of X (which can be identified with mappings from X to \(\{\) 0,1\(\})\) are replaced by so-called fuzzy sets (which by definition, are mappings from X to I). In the same spirit, topological concepts defined in terms of the lattice structure on \({\mathfrak P}(X)\) (ordered by \(A\subset B)\) are replaced by their fuzzy counterparts defined in terms of the lattice structure on \({\mathcal F}(X;I)\) (ordered by \(A\leq B)\). The authors introduce fuzzy filters, explain their convergence and characterize fuzzy topological concepts (such as open sets, closed sets, adherent points and continuity) by means of filter convergence.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 4056525
zbMATH Keywords: fuzzy nets
zbMATH Keywords: fuzzy filters
zbMATH Keywords: filter convergence
author: María Angeles de Prada Vicente
author: Martintxo Saralegi-Aranguren
MaRDI profile type: Publication
cites work: Convergence in fuzzy topological spaces
cites work: Initial and final fuzzy topologies and the fuzzy Tychonoff theorem
cites work: Q4775129
Recommended article: Q4235381
Recommended article: Fuzzy filters in pseudo hoops
Recommended article: Fuzzy filters for image processing
Recommended article: Filters in fuzzy class theory
Recommended article: Fuzzy Clustering-Based Filter
Recommended article: A fuzzy noise-smoothing filter
Recommended article: Semi-Hausdorff fuzzy filters
Recommended article: Q4222499
Recommended article: Q4795632
Recommended article: Q3711321
description: scientific article; zbMATH DE number 4056525