Computational Reasoning Based On Concept Lattices

The theory of concept lattice, proposed by Wille R. in1982, 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 reflects 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.The main results in this thesis are summarized as follows:1. A new concrete computational reasoning method based on concept lattices is proposed.Based on some logical operators, an inclusion degree on concept lattices is defined, which isemployed to define the truth degree of a concept. Some basic properties of the truth mappingare examined. Then a kind of reasoning by computing in the framework of concept lattices isdeveloped.2. In fuzzy concept lattices, we propose a condition under which a fuzzy concept is anα conclution of an assumption subset of L(U, A, I). Then a kind of reasoning by computingin the framework of fuzzy concept lattices is developed.3. Attribute reduction in dual concept lattices is studied. By exploring the relationshipbetween the dual concept lattice and Wille’s lattice, it is proved that the consistent sets in thetwo lattices are the same. Based on the methods of attribute reduction in Wille’s lattice, wepropose an approach to attribute reduction in dual concept lattices.