Object - Oriented (attribute) Concept Lattice And Attribute Reduction Boolean Expression

Formal concept analysis was proposed by Wille R. in 1982. It is a model for data representation and used in finding, ordering and displaying of concepts. Combining with rough set theory, Duntch and Gediga proposed the attribute-oriented concept lattice in 1995 and Y.Y. Yao proposed the object-oriented concept lattice. As an effective tool in knowledge discovery, the theories of object-oriented concept lattice and attribute-oriented concept lattice have been applied in various research areas, such as pattern recognition, information retrieval and data mining.Actually, there are a lot of redundant attributes in the formal context. Therefore, it’s necessary to study the attribute reduction in formal concept analysis. And finding more concise approaches of attribute reduction is an important aspect in the knowledge discovery.In this thesis, based on the logical operations, the object-oriented concept lattice and the property-oriented concept lattice are studied. Furthermore, a novel approach to attribute reduction of concept lattice is investigated. The main results are summarized as follows:1. The logical operations are introduced into formal concept analysis. Up and down approximate operators in Boolean formal context are defined based on the logical operations of Boolean vectors, and the basic properties are also studied. Furthermore, Boolean object-oriented concept lattice and Boolean attribute-oriented concept lattice are proposed based on this pair of approximate operators. The isomorphic between Boolean object(property)-oriented concept lattice and object(property)-oriented concept lattice is proved. It simplify the construction of object(property)-oriented concept lattice.2.In the Boolean concept lattice, the attribute reduction which can preserve the lattice and the one which can preserve the extents of all meet-irreducible elements are proposed. The attribute characters are studied by the relation of Boolean column vectors and the judgment theorems of attribute reduction are presented. Compared with the existing attribute reduction approaches, the one proposed in this thesis is easy to use and with a small amount of computation.