Mathematical aspects of concept analysis
type: Item
instance of: scholarly article
title: Mathematical aspects of concept analysis
zbMATH Open document ID: 0885.06001
DOI: 10.1007/BF02362847
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-03-31T00:00:00Z
review text: In this article the author provides a survey of results related to the mathematical aspects of concept analysis. In an introductory section 1, the subject matter and the basic terminology of contexts, Galois connections, and concepts are introduced. Section 2 contains results about the algebraic problems that arise from the lattice nature of the set of all concepts, in particular, results on the decomposition of concept lattices into smaller ones. Section 3 deals with applications of concepts in data analysis, in particular, on methods of search for dependences between attributes. Algorithmic problems of concept generation are studied in section 4. These include the study of the complexity of enumeration, decision, and classification problems relating to concepts. Section 5 surveys results on the Zarankiewicz problem. There is an extensive bibliography at the end of the article (100 titles). A reader with an interest in this article might also consult the book: Formale Begriffsanalyse (1996; Zbl 0861.06001) by \textit{B. Ganter} and \textit{R. Wille}.
Mathematics Subject Classification ID: 06-02
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 993748
zbMATH Keywords: concept analysis
zbMATH Keywords: contexts
zbMATH Keywords: complete lattices
zbMATH Keywords: decomposition
zbMATH Keywords: algorithm
zbMATH Keywords: complexity
zbMATH Keywords: survey
zbMATH Keywords: data analysis
author: Sergei O. Kuznetsov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02362847
OpenAlex ID: W2033895602
description: scientific article; zbMATH DE number 993748