Dedekind categories with cutoff operators
type: Item
instance of: scholarly article
title: Dedekind categories with cutoff operators
zbMATH Open document ID: 1230.18003
author: Hitoshi Furusawa
author: Yasuo Kawahara
author: Michael Winter
published in: Fuzzy Sets and Systems
publication date: 2011-07-15T00:00:00Z
review text: This paper is concerned with \textit{crispness} of \(L\)-fuzzy relations. It is known that the category of \(L\)-fuzzy relations is a Dedekind category. Since there is no formula in a first-order relational language that characterizes crispness in a Dedekind category [\textit{M. Winter}, Inf. Sci. 139, No.~3--4, 233--252 (2001; Zbl 0992.18004)], so, the authors introduce cutoff operators in this paper to study crispness in Dedekind categories. Cutoff operators are, intuitively, generalizations of the operator that maps a \(L\)-fuzzy relation to the largest crisp relation it contains. A representation theorem is obtained for Dedekind categories with a cutoff operator satisfying the point axiom.
reviewed by: Dexue Zhang
Mathematics Subject Classification ID: 18B10
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 5924599
zbMATH Keywords: Dedekind categories
zbMATH Keywords: fuzzy relation
zbMATH Keywords: crispness
MaRDI profile type: Publication
full work available at URL: j.fss.2010.11.008
OpenAlex ID: W2070817535
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DOI: 10.1016/J.FSS.2010.11.008
description: scientific article; zbMATH DE number 5924599