A note on Zadeh's extensions
type: Item
instance of: scholarly article
title: A note on Zadeh's extensions
zbMATH Open document ID: 0968.54007
DOI: 10.1016/S0165-0114(98)00408-4
published in: Fuzzy Sets and Systems
publication date: 2001-09-18T00:00:00Z
review text: A generalization of the well-known extension principle introduced by Zadeh is discussed. While the extension principle deals with the generalization of the mapping \(f: \mathbb{R}^n\to \mathbb{R}^m\) to fuzzy sets, the study shows that if ``\(f\)'' is continuous then \(f: (F(\mathbb{R}^n), D)\to (F(\mathbb{R}^n), D)\) (where \(F(\mathbb{R}^n)\) is \(a\) the space of compact fuzzy sets) is continuous as well with \(D\) being the supremum over Hausdorff distances between the corresponding level sets.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 1563536
author: Heriberto E. Román-Flores
author: Laécio C. Barros
author: Rodney C. Bassanezi
MaRDI profile type: Publication
cites work: Iterated fuzzy set systems: A new approach to the inverse problem for fractals and other sets
cites work: On generalization of Nguyen's theorem
cites work: A note on fixed points for fuzzy mappings
cites work: On the convergence of fuzzy sets
cites work: On fuzzy metric spaces
cites work: On the equivalence of convergences of fuzzy sets
cites work: A generalization of the Minkowski embedding theorem and applications
cites work: A note on the extension principle for fuzzy sets
cites work: The compactness of \(E(X)\)
cites work: Stability of fixed points set of fuzzy contractions
full work available at URL: s0165-0114(98)00408-4
OpenAlex ID: W2069477530
Wikidata QID: Q128111275
description: scientific article; zbMATH DE number 1563536