The Research Of Uncertainty Measurement Theory And Heuristic Attribute Reduction Algorithm In Rough Set

Rough set theory is a new developed mathematic tool which can deal with uncertain,imprecise and incomplete data[1]. Rough set theory which was proposed by Pawlak in 1982 has been successfully used in machine learning, data mining, decision support and analysis, soft computing, and other fields[2-8].In rough set theory we can divide the domain into different equivalence modules according to different equivalence relations. The more rough the partition is, the greater the module is, and we will get more rough classification; the finer the partition is, the smaller the module is, and we will get more accurate classification. How to measure whether the partition of the universe is rough or finer according to different equivalences and the accuracy of different classification is an important aspect in the theoretical study of rough set theory.Attribute reduction is one of the most important aspect in this theory. Efficient attribute reduction algorithm is the foundation for rough set theory to be applied to knowledge discovery. Rapid attribute reduction algorithm is one of the focuses of the study in rough set theory. How to use the information based on uncertainty measurement theory to simplify the calculation of attribute reduction and get the minimum reduction of attribute set is an important direction of research. It requires an appropriate uncertainty measurement theory, and based on which we can design effective heuristic attribute reduction algorithm, so we need to study the uncertainty measurement theory in rough set theory.In this paper, we define a new measurement of uncertainty—close-degree, which can be used to measure the close degree between two sets. Based on the close-degree of two sets, we give the definitions of partition close-degree of information system, decision-making system, incomplete information system and incomplete decision-making system which can be used to measure the close degree of partition in each system. We give some natures and corresponding theoretical proof of partition close-degree, and redefine attribute importantness according to the partition close-degree in information system, decision-making system, incomplete information system and incomplete decision-making system and design heuristic attribute reduction algorithms of the above system based on partition close-degree of each system.Because the increasement or decreasement of attributes in equivalence relations will lead to the partitions of the universe changed, so we propose two measurements to measure the identify capacity of equivalence relations and give a heuristic attribute reduction algorithm based on the granular entropy. Decision table is a special and important knowledge representation system, the majority of decision-making questions can be expressed in the form of decision table. We give a new method to compute the degree of dependency between decision attributes and condition attributes. Propose an heuristic attribute reduction algorithm based on the degree of dependency with good performance.