Research Of Attributes Reduction And Rules Extraction Of Decision Table Based On Granular Computing

Rough set theory is a new mathematic tool which can deal with uncertain, imprecise and incomplete information. In rough set theory, knowledge is regarded as partitioning the universe, and imprecise knowledge is depicted by using the known knowledge in knowledge base. At present, rough set is widely used in knowledge acquisition, rules generation, decision analysis, intelligent control and so on. Attributes reduction and rules extraction are core of research in rough set theory, and it is significant of seeking for the efficient and fast computing methods about attributes reduction and rules extraction. As the superset of rough set theory, granular computing has covered correlative research about the methods, techniques, and tools with the granularity. Now, granular computing has been a new research hot of artificial intelligence. The development of rough set provides important theory and application model for granular computing.In the theory of granular computing based on rough set, this paper discusses the uncertain measure of knowledge in decision table, and deeply studies the attributes reduction and rules extraction methods. The main innovation of this paper is listed as follows:(1) Aiming at the decision table, we study the partition granularity, namely partition roughness of the decision attributes set relatives to condition attributes set and propose the concept of relative granularity which is used for measuring the discernibility of decision attributes set relatives to condition attributes set in the universe. Then we analyze and prove the monotonous characteristic of the relative granularity, give some properties, and define the measure of relative significance of attributes. On the basis of this theory, we propose a new heuristic attributes reduction algorithm based on relative granularity. By analyzing the example, the algorithm is proved to make up for the shortage of attributes reduction algorithm based on positive region, and it's time complexity is relatively low.(2) To make up for the insufficiency of the rules extraction methods based on the classical rough set theory, this paper studies the rules extraction from decision table based on granular computing. In decision table, we give the expression of the knowledge granular statement, the forming procession of knowledge granular statement and granular computing, and define the concept of sub-granular statement, granular base and so on, then analyze and study the granular base of different level. As the information acquired from real world are complex, noisy or uncertain, so the paper discusses the relation of the knowledge granular statements, analyzes the coverage and confidence of the rules corresponded to the knowledge granular statements, and from different granularity level the paper proposes a new rules extraction algorithm, which tries to extract more decision rules from the granular base of lower level by considering the transformation of different granular level, then the rules derived from the algorithm improve the adaptability ability for noisy data.(3) Aiming at the diversity of the information systems, the paper deeply studies the ordered information systems, incomplete ordered information systems and their decision rules extraction. To effectively deal with the ordered information system, we define the expression of the order relation and extend the strict order relation in incomplete ordered information system by introducing the definition of the extended order relation. Based on order relation, we transform the ordered information system into ordered matrix and give the expression of granular statement and granular operation, then propose a new order rules extraction algorithm for orderd decision table based on granular computing. By using the extended order relation, we turn the incomplete ordered information system into extended order value information table, give some properties and theorems of granular computing in extended order value information table, then aiming at incomplete ordered decision table we propose a new order rules extraction algorithm. Last, the algorithm is proved as effective by analyzing the example.