Attributes Of The Concept Lattice Reduction

Concept lattice also called Formal concept analysis(FCA), is an effective tool for data analysis, FCA has been widely concerned by many researcher. Concept lattice, which based on Formal contexts, describes the association between objects and attributes, and performs conceptual connections between generalization and specialization of formal concepts. So it is widely used in software engineering,data mining and knowledge discovery, etc.Concept lattice, the core data structure in formal concept analysis, we want to gain more concise knowledges from it. Therefore, the attribute reduction in concept lattice is developed. The attribute reduction in concept lattice is an important topic of knowledge discovery. Attribute reduction is through deleting the non-correlated or unimportant attributes to cause the knowledge to express simply and at the same time the basic imformation cannot be losed in view of different goals. Meanwhile, the attribute reduction also becames the important job in extracting rules based on concept lattice. So the study of the attribute reduction in concept lattice has been hot problem in the field of concept lattice. The research of this paper launches from the attribute reduction in concept lattice.First, approaches of attribute reduction in consistent decision formal context focus on using the discemibility matrices and the discernibility function. Based on them, two new methods of attribute reduction in consistent decision formal context are presented. Each of them doesn't depend on the discernibility matrices and the discernibility function. The first new method based on the characters of attributes, reduces the attribute of the consistent decision formal context before building it. This method only relies on the characters of attributes. The second new method based on distinguished function improves the approach based on discernibility function. It causes the attribute reduction in consistent decision formal context become concise.The next in order, The existing research on attribute reduction in concept lattice concentrates in classical concept lattice. There are few works on attribute reduction in non-classical concept lattice. In this paper, based on one of the non-classical concept lattices---information concept lattice, has been done a systematic research. The judgement theorems of consistent set and characters of attributes in information formal context are given. Based on the theory of attribute reduction in information concept lattice, the approaches of attribute reduction in information concept lattice are preliminary discussed.