Granular Reduction of Property-Oriented Concept Lattices

Konwledge reduction on concept lattices is an important research topic in formal concept analysis, and there are some different meanings and methods. This paper mainly studies the granular reduction of property-oriented concept lattices which can preserve the property-oriented concepts, which is called granules in this paper. Firstly, the granules of a property-oriented concept lattice is presented, and it is proven that each extension of property-oriented concepts can be constructed by the granules. Then, the granular reduction of a property-oriented concept lattice is proposed, and the granular discernibility attribute matrix and the granular discernibility attribute function are respectively employed to determine granular consistent sets and calculate granular reducts. Finally, the relation between a granular consistent set and a lattice consistent set of a property-oriented concept lattice is discussed.