DocumentCode :
1603195
Title :
Operators and spaces associated to matrices with grades and their decompositions
Author :
Belohlavek, Radim ; Konecny, Jan
fYear :
2008
Firstpage :
1
Lastpage :
6
Abstract :
We present results on decompositions of matrices with grades, i.e. matrices I with entries from a bounded ordered set L such as the real unit interval [0,1]. We consider decompositions of an n x m matrix I into a circular and triangular product A * B of an n x k matrix A and a k x m matrix B with k as small as possible. This problem generalizes the decomposition problem of Boolean factor analysis in which a decomposition of a binary matrix is sought into two binary matrices and which is a particular case of our setting when L has just two elements, namely 0 and 1. In our previous work, we proved that formal concepts of concept lattices associated to I are optimal factors for such decompositions. In this paper, we investigate concept-forming operators and concept lattices associated to decompositions of matrices and implications of these results.
Keywords :
Boolean algebra; mathematical operators; matrix decomposition; set theory; Boolean factor analysis; binary matrix decomposition problem; bounded ordered set; concept-forming operator; formal concept lattice; Fuzzy logic; Information processing; Lattices; Matrix decomposition;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Fuzzy Information Processing Society, 2008. NAFIPS 2008. Annual Meeting of the North American
Conference_Location :
New York City, NY
Print_ISBN :
978-1-4244-2351-4
Electronic_ISBN :
978-1-4244-2352-1
Type :
conf
DOI :
10.1109/NAFIPS.2008.4531254
Filename :
4531254
Link To Document :
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