Degrees of compactness in fuzzy convergence spaces
type: Item
instance of: scholarly article
title: Degrees of compactness in fuzzy convergence spaces
zbMATH Open document ID: 0994.54008
DOI: 10.1016/S0165-0114(01)00016-1
author: G. Jäger
published in: Fuzzy Sets and Systems
publication date: 2002-05-21T00:00:00Z
review text: In [ibid. 92, No. 3, 349-355 (1997; Zbl 0968.54502)] the author introduced a notion of compactness for fuzzy subsets of fuzzy convergence spaces in the sense of [\textit{E. Lowen}, \textit{R. Lowen}, and \textit{P. Wuyts}, ibid. 40, No. 2, 347-373 (1991; Zbl 0728.54001)]. The aim of this paper is to define the measure of compactness of a fuzzy set in a fuzzy convergence space -- that is to assign to a fuzzy set a certain number \(\alpha \in [0,1]\) characterizing ``to what degree this fuzzy set is compact''. The definition of the degree of compactness relies on the concept of residual implication which allows ``to fuzzify'' the crisp subsethood relation. The theory which is being developed in the paper generalizes at the same time the theory of compactness for fuzzy convergence spaces worked out by the author earlier and some measures of compactness in (Chang) fuzzy topological spaces introduced by Lowen. Among others, the author is interested in applying the notion of degree of compactness for the study of function spaces in fuzzy topology.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 1743120
zbMATH Keywords: measure of compactness of a fuzzy set
zbMATH Keywords: fuzzy convergence space
zbMATH Keywords: degree of compactness
reviewed by: Alexander Šostak
MaRDI profile type: Publication
cites work: A generalised form of compactness in fuzzy topological spaces
cites work: Q4121153
cites work: Compactness in fuzzy convergence spaces
cites work: The Richardson compactification for fuzzy convergence spaces
cites work: Compactness and connectedness as absolute properties in fuzzy topological spaces
cites work: Q4231001
cites work: Relative compact fuzzy subsets in fuzzy convergence spaces
cites work: On fuzzy function spaces
cites work: Compactness in fuzzy function spaces
cites work: Pointwise convergence, continuous convergence and even continuity in FNS
cites work: Even continuity and equicontinuity in fuzzy topology
cites work: Q3965241
cites work: Fuzzy topological spaces and fuzzy compactness
cites work: Convergence in fuzzy topological spaces
cites work: Mathematics and fuzziness, some personal reflections
cites work: On measures of compactness in fuzzy topological spaces
cites work: Q4010278
cites work: The categorical topology approach to fuzzy topology and fuzzy convergence
cites work: Q3336431
cites work: Q3779408
description: scientific article; zbMATH DE number 1743120