Research On Rough Set Methodology Of Interval-valued Information Systems

In 1982, Rough Set Theory, a mathematical theory used to deal with uncertain knowledge, was introduced by Poland scholar Professor Z. Pawlak. With rough set theory, inexactness, uncertainty and the incomplete information can be effectively analyzed and processed, and the knowledge and rules hidden in data can be revealed. By three decades development, rough set theory has become a very important branch of artificial intelligence, especially intelligent information processing, and has been successfully used in wide fields such as machine learning, pattern recognition, decision analysis, process control, knowledge discovery in database, expert system etc.The attribute reduction is a very important issue in rough set theory. The methods based on indiscernibility matrix and many heuristic algorithms based on the attribute importance are proposed for attribute reduction in the existing researches. In this thesis, a new concept of an approximation space mapping is introduced, and its properties are discussed. Some relationship between approximation space mapping and attribute redundancy is established. Based on approximation space mapping, a new algorithm for finding an approximate reduction or a relative reduction of an attribute set is proposed.The interval_valued information system, as a framework for data description, is used in wide fields of scientific research and engineering. Most researches on interval_valued information systems, such as decision rule acquiring and reasoning, are based on interval number ordering. For knowledge acquirement in interval_valued information systems, a kind of similarity relation on the universe for depicting the indiscernibility between two objects is proposed in the paper. By dint of the concept of a maximal consistent block, the lower and upper approximations of a target concept are defined, and the approximation accuracy is discussed. Some methods of attribute reduction, reduction on an object for data compression and rule extraction in interval_valued information systems are presented in this thesis.