The Research Of Attribute Reduction In Rough Sets And Concept Lattices

Rough set theory, proposed by Pawlak in 1982, is a mathematical theory used in data analysis. The theory of Concept lattice (also called formal concept analysis), proposed by Wille in the same year, is a tool for creating and arranging of concepts. As two powerful tools in data analysis and knowledge discovery, rough set theory and concept lattice theory have paid much attention of artificial intelligence researchers all over the world.At present, the two theories have been applied in many research areas, such as software engineering, data mining, information retrieve, machine learning, uncertain rule capturing and decision administering, and so on.Attribute reduction is an important aspect in knowledge discovery. In this thesis, by using of the theory of attribute reduction in information system and in concept lattice, we propose a new method of attribute reduction in decision tables based on closed operators and a new method of reduction in concept lattice which is different from the one in [29]. Furthermore, we study the properties of two similar formal contexts under homomorphism. The main results in this thesis are summarized as follows:1. A closed-operator-based approach to attribute reduction of decision tables is proposed. For a consistent decision table, attribute reduction is studied from the point of view of congruence relations on the condition attribute set and its power set. The properties of two closed set families C_r and C_R are discussed, and the relationship between the two families is established, from which we obtain the sufficient and necessary conditions for C_r = C_R. A new method to attribute reduction of decision tables is then proposed under the condition C_r = C_R. It is proved that the new concept of attribute reduction is equivalent to the those introduced in [12,28].2. A new method of attribute reduction in concept lattice is proposed. Based on the reduction theory of concept lattice in [29], we obtain some minimal attribute set families by using all the intersection irreducible elements in concept lattice. Select one attribute from each intersection irreducible elements and merge, then the union is a reduct of the formal context defined in [29]. At the same time, the relative algorithm is developed.3. The relations between elements of two similar formal contexts are studied under a homomorphism. For a formal context, the properties of concepts and consistent sets under a homomorphism are analyzed. For a formal decision context, the properties of consistency under homomorphism are discussed, and the sufficient and necessary conditions for that the homomorphic image of a reduct is also a reduct are developed.