The Attribute Reduction And Extend Mode Of Concept Lattice

Concept lattice is an effective tool for concept discovery from data, having the ability to embody relationship of concepts in a vivid and concise way using hasse diagram. Concept lattice has been widely used in information retrieval, digital library, software engineering and knowledge discovery. Rough set theory can analyse and deal with the imprecise, inconsistent and incomplete information. Fuzzy set theory can deal with the fuzzy information.They all have been applied to a lot of fields successfully.In this article, firstly through the research of the properties of concept lattice, we difine the Boolean concept lattice and shows some properties of it. Secondly, we discuss the extend mode of the concept lattice. On the one hand, through the study of two approximation operators in the rough sets theory, one can obtain a new concept lattice--# concept lattice, and compare with the differences and relations of several kinds of concept lattices. On the other hand, With extending the binary relation of the formal context to a fuzzy relation, the fuzzy formal context can be defined , and the fuzzy formal concept and the formal concept lattice can also be defined. Finally, we introduce the concept of attribute reduction in rough set theory to attribute reduction of the formal context and corresponded concept lattice, then give two kind of arithmetic by using distinguishable attribute matrix.