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**Relating attribute reduction in formal, object-oriented and property-oriented concept lattices.**
*(English)*
Zbl 1268.06007

Summary: Attribute reduction is an important step in reducing computational complexity in order to extract information from relational systems.

Three of these systems are the formal, object-oriented and property oriented concept lattices. Attribute reduction in the last two concept lattices has recently been studied. The relation with the first concept lattice is very important since two important, independent tools to extract information from databases – the formal concept analysis and rough set theory – will be related. This paper studies attribute reduction in these three frameworks. The main results are that the classification of each attribute into absolutely necessary, relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduct in one of these relational systems is also an attribute reduct in the others.

Three of these systems are the formal, object-oriented and property oriented concept lattices. Attribute reduction in the last two concept lattices has recently been studied. The relation with the first concept lattice is very important since two important, independent tools to extract information from databases – the formal concept analysis and rough set theory – will be related. This paper studies attribute reduction in these three frameworks. The main results are that the classification of each attribute into absolutely necessary, relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduct in one of these relational systems is also an attribute reduct in the others.

### MSC:

06B23 | Complete lattices, completions |

06A15 | Galois correspondences, closure operators (in relation to ordered sets) |

68T30 | Knowledge representation |

### Keywords:

Galois connection; formal concept analysis; object-oriented concept lattices; property-oriented concept lattices; attribute reduction
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\textit{J. Medina}, Comput. Math. Appl. 64, No. 6, 1992--2002 (2012; Zbl 1268.06007)

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