Cut systems in sets with similarity relations
type: Item
instance of: scholarly article
title: Cut systems in sets with similarity relations
zbMATH Open document ID: 1225.03070
author: Jiří Močkoř
published in: Fuzzy Sets and Systems
publication date: 2011-01-31T00:00:00Z
review text: Fuzzy sets with values in a complete lattice \(L\) can be defined either by means of membership functions, or, equivalently, by means of nested systems of \(\alpha\)-cuts. This paper is focused on finding some analogies between the second approach and some nested systems of subsets defined in sets with similarity relations. Special \(f\)-cut systems are introduced and their properties and category-theoretic isomorphic objects are discussed. Moreover, a first-order fuzzy logic interpretations in cut systems are discussed, proving, among others, some relationships between classical interpretations in sets with similarity relations and interpretations using nested systems.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 5843060
zbMATH Keywords: similarity relation
zbMATH Keywords: fuzzy sets in sets with similarity relations
zbMATH Keywords: \(\alpha \)-cut systems
zbMATH Keywords: models of fuzzy logic
MaRDI profile type: Publication
full work available at URL: j.fss.2010.07.009
OpenAlex ID: W2133809731
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DOI: 10.1016/J.FSS.2010.07.009
description: scientific article; zbMATH DE number 5843060