Matrix-based Approach For Optimal Approximation And Its Incremental Updating

Rough set theory provides theoretical framework for data mining and knowledge discovery.In rough set theory,a rough set can be approximated by a pair of precise sets(upper and lower approximation).But there is a set,which is more similar to the target concept than the upper-approximation or lower-approximation.The concept of optimal approximation has been proposed by some scholars.This paper takes the classical rough set model as the background and uses the relation matrix as a tool to study the matrix calculation of the optimal approximation and its incremental update.The main contents are as follows:Due to matrix have characters of intuitive and easier to calculate,the paper presents a method for using the relation matrix to obtain the optimal approximation of the target set.Firstly,the relation matrix corresponding to the equivalent relationship determined by the attributes in the classical information system.Combining the target set,the basic vector corresponding to the target set is derived by matrix operation.Secondly,by using the importance of the basic vector and the equivalence class,all the equivalence classes which constitute the optimal approximation are further determined.Finally,an algorithm is designed to find the optimal approximation by using the relation matrix and an example shows that the algorithm is effective in calculating the optimal approximation.Because data changes dynamically in real-world applications,this thesis studies the incremental update problem of the optimal approximation from four aspects: adding a single attribute,adding multiple attributes,adding a single object,and adding multiple objects.And separately designing matrix algorithms for optimal approximate incremental updating.These algorithms are shown to be effective through examples.