The Research On Attribute Reduction In Decision Formal Context

The theory of concept lattice, proposed by Wille R. in 1982, is also called the theoryof formal concept. The concept lattice sets up a kind of relation of conceptual hierarchiesaccording to relations among data, and it vividly re?ects relationship of generalization andspecialization among concepts. As a useful tool in data analysis and knowledge management,many scholars devote themselves to the study of concept lattice. Now concept lattices have beenapplied in many research areas, such as data mining, software engineering, machine learningand information retrieving and so on.Attribute reduction is one of the key problems in the study of concept lattice theory. In thisthesis, we propose some new concepts of attribute reduction in decision formal concept and infuzzy environment based on some earlier results in [6],[7]. The main results in this thesis aresummarized as follows:1. An approach to irr-attribute reduction based on irreducible element in concept latticesof a consistent decision formal context and an inconsistent decision formal context is proposed.A irr-consistent set is defined which contains all the irreducible elements of object-orientedconcepts. It is compared with the original consistent set defined by Zhang~[3]. Then sufficientcondition of discriminating irr-consistent set is obtained. Finally, attribute reduction in conceptlattices of an inconsistent decision formal context is also studied.2. Attribute reduction of a decision formal context under a homomorphism is studied.Homomorphism consistent set is defined and an approach to attribute reduction of a consistentdecision formal context based on concept lattices from the view of homomorphism is discussed.It is proved that homomorphism reduct is equivalent to the original reduct proposed by Zhang[3].As a result, Boolean method is formulated by constructing discernibility matrix.3. Attribute reduction of fuzzy decision formal context is investigated. A kind of fuzzydecision formal context is proposed, in which a (α,β) consistent set and reduct are defined.Judgement theory to determine, consistent set and reduct of fuzzy decision formal context areobtained.