On efficient factorization of standard fuzzy concept lattices and attribute-oriented fuzzy concept lattices

We propose two ways to make factorization of attribute-oriented fuzzy concept lattices recently studied by Ciobanu & Văideanu more efficient. Firstly, we show that the blocks of the corresponding factor lattice are determined by a particular fuzzy interior operator. This allows us to compute an...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 351; pp. 108 - 121
Main Author: Konecny, Jan
Format: Journal Article
Language:English
Published: Elsevier B.V 15.11.2018
Subjects:
Concept lattice
Factorization
Formal context
Fuzzy sets
Similarity
Fuzzy sets
Similarity
Concept lattice
Factorization
Formal context
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:We propose two ways to make factorization of attribute-oriented fuzzy concept lattices recently studied by Ciobanu & Văideanu more efficient. Firstly, we show that the blocks of the corresponding factor lattice are determined by a particular fuzzy interior operator. This allows us to compute an attribute-oriented fuzzy concept lattice by intents. Such a computation requires fewer traversals through data, as the number of the attributes is usually smaller than the number of objects. Secondly, we scale the input data in such a way that the factor lattice can be computed as a one-sided fuzzy-crisp concept lattice. Our experiments indicate that both methods lead to a significant improvement in efficiency of computation of the factor lattice. In addition, we improve and extend the theory provided by Ciobanu & Văideanu.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2018.01.012