Attribute Reduction Based On Relations And Set Approximations In Concept Lattices

The theory of rough sets was originally proposed by Pawlak Z. in 1982 as a mathematical approach to handle imprecision, vagueness, and uncertainty in data analysis. It has recently received wide attention in real-life applications and theoretical research. By using the concepts of lower and upper approximations in rough set theory, knowledge hidden in information systems may be unravelled and expressed in the form of decision rules. Concept lattice theory, also called formal concept analysis, proposed by Wille R. in the same year, is a method for data analysis used in finding ordering and displaying of concepts. A concept lattice is an ordered hierarchy that is defined by a binary relation between objects and attributes in a data set. Each formal concept is an object-attribute pair, which consists of two parts: the extension and intension. Recently, the two theories have been applied in various research areas, such as data mining, machine learning, expert system, decision analysis, computer network, software ngineering, and so on.Knowledge reduction is an important aspect in knowledge discovery. It is therefore an important part in the study of rough set theory and formal concept analysis. This thesis studies attribute reduction in formal concept lattices and rough approximations of a set in a formal context. The main results and originalities are summarized as follows:1. By employing the characteristics of different type of attribute, we propose a method of attribute reduction in concept lattices.2. From the point of view of dependence spaces, two equivalent approaches of attribute reduction for a formal context and an information system are proposed, respectively.3. We introduce some new concepts of dominance reduction in formal context and decision formal context. Some basic properties of these concepts are discussed, and a method of dominance reduction is proposed by using the discernibility attribute set.4. Finally, we study rough approximations in formal contexts. A novel concept of similarity approximation operator is proposed, and the properties of the approximation operators are discussed. The aximatic characterization of this operator is then examined.