Study On The Approaches For Updating Approximations Dynamically Based On Set-Valued Rough Sets

Rough set theory is a mathematical method for processing inconsistent data. It has been successfully applied in machine learning, decision analysis and data mining. But it requires that the data in the information system must be accurate and complete. In the real life, the data varies continuously and gets more and more complicated, so the classific rough set theory no longer meets the practical needs. The set-valued rough set theory, as an extension of the classific rough set theory, can deal with the data missing and incomplete data. Therefore, it is meaningful to study how to update the knowledge in the dynamical information system and aid our decision making.This thesis focuses on how to update the approximations incrementally under the set-valued rough set theory when the objects and the attributes change dynamically. Firstly, we discuss the incrementally methods for updating approximations under the condition that the attribute set is unchanged and objects vary. When objects are added, we research on the set-valued information system and the set-valued decision making system. By comparing the consistency between the newly added object with the original one, we get to know whether the concept (or the decision class in the set-valued decision making system) changes or not. Thus we update the approximations incrementally. When objects are deleted, we firstly decide whether the object belongs to the concept or not. Then we compare the consistency between this object and the other objects. Finally, we update the approximations. The experimental evaluation has been conducted to verify the effectiveness of our methods.Secondly, we study the case when the object set is unchanged and the attribute set varies. We discuss the incrementally methods for updating approximations while attributes increase or decrease. When an attribute is added or deleted, we study the relationship between the consistent class and the concept and the relationship among the consistent classes, approximations and the boundary region. We propose some theorems and investigate their corresponding properties of updating approximations incrementally while adding or deleting attributes. Thus we design the methods for updating approxmimations incrementally along with the increase or decrease of attributes. Examples and experiments are exployed to verify the effectiveness of the methods.