The Study Of Approaches And Applications Of Knowledge Reduction In Incomplete Information Systems

In 1982, Poland mathematician Pawlak proposed the concept of rough sets. Rough set theory is a mathematical tool to deal with uncertainty and incomplete information, which provides a new approach for the analysis and process of uncertainty data. The theory of concept lattice was initiated by German mathematician Wille in 1982, which is an effective tool of knowledge representation. Rough set theory and the theory of concept lattice complement each other, they are closely related.Attribute reduction is a key problem in the knowledge discovery in information systems. Also, it is one of the core problems of rough set theory. Different kinds of attribute reduction theories and approaches were proposed with respect to complete information systems. As for incomplete information systems, the related researches are still not perfect. In this paper, based on rough set theory and the theory of concept lattice, we study the attribute reduction theory, attribute reduction methods and attribute reduction algorithms of incomplete information systems. Furthermore, we apply our theoretical results to the field of radio signal recognition. The main results and innovations in this thesis are summarized as follows:1. The approximation operators based on reflexive and transitive relation in generalized rough set model are studied, compactness condition (COMP) about topology structure is proposed. It is proved that there is a one to one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfies (COMP). In complete completely distributive lattice, the concept of neighborhood is presented based on covers. Furthermore, new upper approximation operators and lower approximation operators are proposed based on the neighborhood, and some basic properties are derived.2. According to actual situation of missing data in the incompletely information systems, a new kind of indiscernibility relation is proposed based on contribution degree of attributes; the relationships between it and the other indiscernibility relations are discussed. Based on the similarity relation proposed by Stefanowski, a new method of attribute reduction based on important degree of attributes is presented; attributes reduction algorithms with respect to incompletely information and incompletely decision table are proposed, respectively.3. For incompletely decision table, based on the generalization similarity relation, equivalent characterization conditions and reduction judging theorems of distribution consistent set and positive region consistent set are given; methods of distribution reduction and positive region reduction are given by discernibility matrix and discernibility function.4. Similarity relation of attributes in formal context is proposed, reduction characterization and reduction approach of attributes are discussed in concept lattice. Based on the similarity relation of attributes and topology structure of the set of attributes, a method of formal concept generation is given. MATLAB experiments show that the method is effective. 5. We apply our theoretical results to the field of radio signal recognition. The information system and formal context of radio signal are constructed, and the methods of features extraction and rules mining are proposed. Experiments show these methods are effective and reasonable.