The fuzzy theory based on AFS algebras and AFS structure
type: Item
instance of: scholarly article
title: The fuzzy theory based on AFS algebras and AFS structure
zbMATH Open document ID: 0896.06007
author: J. Ning
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-10-01T00:00:00Z
review text: Let \(X,M\) be sets. The triple \((M,\tau,X)\) is called an AFS structure, where \(\tau= X\times X\to 2^M\) satisfying some conditions. After adding a \(\sigma\)-algebra \(\sigma\) and a positive measure over \(\sigma\), the author establishes the notions of semi-cognitive fields and cognitive fields. Based on these structures, the author defines a membership function and gives the definition of a fuzzy variable. The author believes that people can use mathematical analysis to study such a fuzzy theory and to process fuzzy information.
Mathematics Subject Classification ID: 06B99
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 1115480
zbMATH Keywords: lattices
zbMATH Keywords: AFS structure
zbMATH Keywords: cognitive fields
zbMATH Keywords: membership function
zbMATH Keywords: fuzzy variable
reviewed by: Yingming Liu
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5718
OpenAlex ID: W2014433834
cites work: Q4308448
cites work: Q4308449
cites work: Q4868285
cites work: Q4868286
cites work: The fuzzy sets and systems based on AFS. structure, EI algebra and EII algebra
cites work: A new fuzzy model of pattern recognition and hitch diagnoses of complex systems
cites work: Q3222326
cites work: Q4143304
DOI: 10.1006/JMAA.1997.5718
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description: scientific article; zbMATH DE number 1115480