Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued ``intuitionistic'' sets, ``intuitionistic'' fuzzy sets and topologies
type: Item
instance of: scholarly article
title: Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued ``intuitionistic'' sets, ``intuitionistic'' fuzzy sets and topologies
zbMATH Open document ID: 1084.03042
author: Javier Gutiérrez García
author: S. E. Rodabaugh
published in: Fuzzy Sets and Systems
publication date: 2006-01-24T00:00:00Z
review text: This is a category-theoretically based study of the appropriateness of different recent ``generalizations'' of the notion of fuzzy set. The authors prove that almost all of these generalizations of the standard notion of fuzzy set with the real unit interval as the membership degree structure become theoretically obsolete from the unifying point of view that the membership degree structures for fuzzy sets should be lattices, possibly enriched with additional operations like in the very popular case of residuated lattice-ordered semigroups. What remains, therefore, as motivations for such particular ``generalizations'' should be careful discussions what is needed for particular applications, a topic which quite often is extremely underrepresented in ``theoretical'' papers related to such ``generalizations''.
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 5001361
zbMATH Keywords: interval-valued sets
zbMATH Keywords: intuitionistic fuzzy sets
zbMATH Keywords: grey sets
zbMATH Keywords: redundancy of notions
zbMATH Keywords: semi-polarity
zbMATH Keywords: semi-De Morgan algebras
zbMATH Keywords: fuzzy topology
zbMATH Keywords: double fuzzy topology
zbMATH Keywords: order-isomorphism
zbMATH Keywords: functorial isomorphism
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
full work available at URL: j.fss.2005.05.023
OpenAlex ID: W2003364577
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DOI: 10.1016/J.FSS.2005.05.023
description: scientific article; zbMATH DE number 5001361