On Knowledge Acquisition In Incomplete Multi-Scale Ordered Decision Systems

With the popularity of the Internet and the arrival of the era of big data, the method of data mining has become a main research direction for many scholars. As an important mathematical method for data mining and knowledge discovery, the theory of rough sets, which can be used to deal with incomplete, imprecise and inconsistent data, 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, knowledge discovery in databases, and, especially, in the analysis of agricultural data. Granular computing, 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. The data mining method based on rough set theory and granular computing has become research hotspot recently.In traditional rough set data analysis, each object under each attribute in an information table can only take on one value. Such an information table is called a single scale information table. However, objects are usually measured at different scales under the same attribute. Thus, in many real-life multi-scale information tables, an object can take on as many values as there are scales under the same attribute. Moreover, we are often faced with the problems for the ordering of objects according to the ordering of properties of the considered attributes and attribute values for some objects are unknown. And knowledge representation and knowledge discovery in multi-scale ordered information tables in which attribute values for some objects are unknown is crucial in decision making. Such a system is called an incomplete multi-scale ordered information table. The traditional rough set approach for such information table may not be applicable. Therefore, to explore new extended rough set model for analyzing information granules and knowledge acquisition in incomplete multi-scale ordered decision table is an important issue.In this dissertation, information granules and knowledge acquisition in incomplete multi-scale ordered decision tables from the perspective of granular computing are studied. The notion of incomplete multi-scale ordered information systems is first introduced, and rough set approximations and attribute reduction in incomplete multigranular ordered information systems are also discussed. The concept of incomplete multi-scale ordered decision systems is then proposed. Dominance relations corresponding to each conditional attribute set and the decision attribute in incomplete multi-scale ordered decision systems are respectively defined. Discernibility matrix in incomplete multi-scale ordered decision systems is further explored, and the approach to attribute reduction in incomplete 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 in incomplete multi- scale ordered decision systems is analyzed.