Knowledge Acquisition Theory And Method Of Concept Lattice Based On Visual Graph

Formal concept analysis, proposed by German mathematician Wille in 1982, is used in knowledge discovery and data mining. At present, there are many re-sults in formal concept analysis and it has been widely applied to many fields, for example, expert system, decision analysis and machine learning.The dissertation mainly studies the acquisition of approximate concepts, the judgment of irreducible elements based on pictorial diagrams, the method of con-structing four types of lattice reduction, and the consistency and the reduction of formal decision contexts. The main results and originalities in this dissertation are summarized as follows:(1) The approximate concepts associated with objects and attributes are ob-tained by defining k-grade relations on the object set and the attribute set of a formal context. Firstly, the relationship between the k-grade relations and equiv-alent relation is studied. And, the related definitions of approximate concepts are proposed. Then, it is proved that the corresponding approximate concepts are for-mal concepts, object oriented concepts and property oriented concepts when k is granted with a special value. Lastly, these approximate concepts are explained by a example.(2) Based on pictorial diagrams, the approach to obtaining approximate con-cepts is proposed. For a formal context, the definitions of object pictorial diagram and property pictorial diagram are introduced. Then, the concrete methods of ac-quiring approximate concepts are given according to the two kinds of pictorial diagram. In addition, the transformation between formal concepts (object oriented concepts, property oriented concepts) and the elements of pictorial diagrams is studied.(3) The new judgment theorems of irreducible elements are studied. For a concept lattice and a property oriented concept lattice, the judgment theorem of join-irreducible elements are proposed on the basis of the object pictorial diagram. For a concept lattice and an object oriented concept lattice, the judgment theo-rem of meet-irreducible elements and join-irreducible elements are then proposed based on the property pictorial diagram, respectively. Furthermore, the judgment theorem about the double irreducible element of a concept lattice is obtained. Fi-nally, for concept lattices, complementary context concept lattices, property ori-ented concept lattices and object oriented concept lattices, the new methods to their reduction are proposed based on the property pictorial diagram.(4) The consistency and the reduction of formal decision contexts are studied. For a formal decision context, according to the condition property pictorial diagram and the decision property pictorial diagram, the judgment theorem to the strong consistent and the weak consistency are given, based on which, the new methods to the reduction in order to keep the corresponding consistency of formal decision contexts are proposed.