Ytow, Nozomi; Morse, David R. and Roberts, David McL.
(2006).
*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 |
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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 Mathematics, Computing and Technology |

Interdisciplinary Research Centre: | Centre for Research in Computing (CRC) |

Item ID: | 5441 |

Depositing User: | David Morse |

Date Deposited: | 21 Sep 2006 |

Last Modified: | 14 Jan 2016 16:13 |

URI: | http://oro.open.ac.uk/id/eprint/5441 |

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