On the equivalence of convergences of fuzzy sets
type: Item
instance of: scholarly article
title: On the equivalence of convergences of fuzzy sets
zbMATH Open document ID: 0873.54007
DOI: 10.1016/0165-0114(95)00182-4
author: Heriberto E. Román-Flores
author: Rojas-Medar Marko Antonio
published in: Fuzzy Sets and Systems
publication date: 1997-10-12T00:00:00Z
review text: Let \(\{u_n\}\) be a sequence of fuzzy sets with compact nonempty level sets and \(u\) be a fuzzy set, which in addition has continuous level sets i.e. \(\alpha \to L_\alpha (u)\) is continuous in the Hausdorff metric. Here \(L_\alpha(u)\) denotes the \(\alpha\)-level set of \(u.\) In the paper the authors characterize the convergence of \(\{u_n\}\) to \(u\) in the metric \(H(u,v)= \sup_{0\leq\alpha\leq 1}h(L_\alpha (u),L_\alpha (v)).\) For related results see also \textit{P. Diamond} and \textit{P. Kloeden} [Metric spaces of fuzzy sets (1994; Zbl 0873.54019)].
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1022513
zbMATH Keywords: metric
zbMATH Keywords: levelwise and variational convergence
reviewed by: Osmo Kaleva
MaRDI profile type: Publication
full work available at URL: 0165-0114(95)00182-4
OpenAlex ID: W2022279410
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Wikidata QID: Q127360895
description: scientific article; zbMATH DE number 1022513