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Rough Set Approximation as formal concept

Ytow, Nozomi; Morse, David R. and Roberts, David McL. (2006). Rough Set Approximation as formal concept. Journal of Advanced Computational Intelligence and Intelligent Informatics, 10(5) pp. 606–611.

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Abstract

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

Item Type: Journal Article
ISSN: 1343-0130
Extra Information: Journal special issue on Rough Sets and Granular Computing.
Keywords: dual isomorphism; taxonomy; multiple hierarchy; concept comparison; concept analysis
Academic Unit/Department: Mathematics, Computing and Technology > Computing & Communications
Interdisciplinary Research Centre: Centre for Research in Computing (CRC)
Item ID: 5441
Depositing User: David Morse
Date Deposited: 21 Sep 2006
Last Modified: 02 Dec 2010 19:54
URI: http://oro.open.ac.uk/id/eprint/5441
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