Knowledge Discovery On Multi-scale Ordered Information Systems

Rough set theory, which deals with incomplete information of data, was initiated by Pawlak in the early 1980 s. As a new kind of mathematical theory, the main idea of rough set theory is to make decision or classification in information systems with keeping the ability of classification. It has become a fast growing field of research in the past three decades. As an important mathematical method for data mining, rough set theory has been found to have very successful applications in the fields of artificial intelligence such as expert systems, machine learning, pattern recognition, decision analysis, process control, and knowledge discovery in databases. It has also been applied widely in industrial and agricultural fields.Granular computing(Gr C), which imitates human being’s thinking, is an approach for knowledge representation and data mining. Its basic computing unit is called granules, and its objective is to establish effective computation models for dealing with large scale complex data and information. Rough set theory is one of the most advanced approaches that popularize Gr C, it enables us to precisely define and analyze many notions of Gr C. Most applications of Gr C based on rough set theory belong to the attribute-value representation model. The traditional rough set theory is based on a single scale information system in which each object under each attribute can only take on one value, however, objects are usually measured at different scales under the same attribute, in many real-life multi-scale information systems, an object can take on as many values as there are scales under the same attribute. One has to observe and analyze data, and make decision in such information systems. Thus, the concept of multi-scale information systems was introduced, and many researchers had paid attention to study knowledge representation and knowledge acquisition in multi-scale information systems.In this dissertation, based on the concept of granular computing, the data sorting and knowledge acquisition in multi-scale information systems and multi-scale ordered information systems are proposed. The concept of multi-scale ordered information systems is first introduced and a dominance relation corresponding to each attribute set is defined. Lower and upper approximations based on dominance relations with different levels of granulation are further defined and their properties are examined. The notion of Discernibility matrix in multi-scale ordered decision systems is then defined, the approach to attribute reduction in multi-scale ordered decision systems is also proposed. Finally, with reference to different levels of granulations, knowledge acquisition in the sense of If-Then rules is analyzed.