An early approach toward graded identity and graded membership in set theory
type: Item
instance of: scholarly article
title: An early approach toward graded identity and graded membership in set theory
zbMATH Open document ID: 1216.03059
published in: Fuzzy Sets and Systems
publication date: 2011-01-31T00:00:00Z
review text: Fuzzy sets were introduced by \textit{L. A. Zadeh} in [Inf. Control 8, 338--353 (1965; Zbl 0139.24606)]. Independently and in the same year, German mathematician D. Klaua introduced a rather similar concept of a theory with graded membership predicates and graded equality relations. While Zadeh's idea has grown up enormously, Klaua's approach ran dry in a few years. This paper speculates why Klaua himself stopped to develop his theory. In the context of logics of left-continuous triangular norms (so-called MTL-logics), some properties of Klaua's graded relations are discussed. Moreover, simultaneous recursive definitions of these relations are compared with a rather similar approach introduced by Scott and Solovay in 1967.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03-03
zbMATH DE Number: 5843021
zbMATH Keywords: fuzzy set theory
zbMATH Keywords: universes of fuzzy sets
zbMATH Keywords: mathematical fuzzy logic
zbMATH Keywords: graded identities
zbMATH Keywords: Boolean-valued universes
Wikidata QID: Q56093398
author: Siegfried J. Gottwald
MaRDI profile type: Publication
full work available at URL: j.fss.2009.12.005
OpenAlex ID: W2063038240
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DOI: 10.1016/J.FSS.2009.12.005
description: scientific article; zbMATH DE number 5843021