2013•International Journal of Wavelets Multiresolution and Information ProcessingRequires access

ATTRIBUTE REDUCTION OF CONCEPT LATTICE BASED ON IRREDUCIBLE ELEMENTS

Tong-Jun Li, Ming-zhi Li, Yu Qiang Gao

Abstract

Attribute reduction of formal context is a crucial reseach issue in formal concept analysis. In this paper, based on the meet-irreducible elements and join-irreducible elements of concept lattice, two kinds of attribute reductions of formal context are proposed, which are called MI-attribute reduction and JI-attribute reduction. Subsequently, we discuss the relationships among them and two existing attribute reductions of formal context, lattice-based attribute reduction and granular reduction. Consequently, we find that the MI-attribute reduction and lattice-based attribute reduction are identical. For JI-attribute reduction, the judgement theorems of JI-consistent attribute sets are obtained. Finally, by using the discernibility attribute sets, a method of computing all JI-attribute reducts of a formal context is presented.

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Key concepts: Attribute domain, Formal concept analysis, Lattice Miner, Reduction (mathematics), Rough set, Lattice (music), Lattice reduction, Mathematics