Matrix Representation Of Rough Sets Theoryand Its Application In Attribute Reduction

With the social progress and the rapid development of technology, people enjoy a variety of convenience brought by the information age, but be overwhelmed by the massive data. It is a urgent problem to how to discover knowledge effectively and timely form massive data. It is necessary to speed up the process of knowledge discovery in order to mining the effective information. Rough set has been successfully applied in pattern recognition,artificial intelligence,data mining and other fields,because it does not need too much prior knowledge. In the rough set,the core idea is that The imprecise,vague question are described by known knowledge. The precise upper and lower approximation describe imprecise knowledge to understand imprecise knowledge. This paper is based on matrix representation and matrix calculation to study the calculation of approximation operators of rough set model. The main research contents of this paper are as follows:This paper firstly introduces matrix calculation of probability rough set model’s upper and lower approximation. The upper and lower approximations of probability rough set model can be obtained from the matrix calculation among the equivalence relation matrix, sectional matrix and the column matrix of unknown knowledge. A principles and an algorithm for computing upper and lower approximation is given. The matrix calculation of upper and lower approximation is also given when probability rough set model extends to probability rough set model under fuzzy relations.The definition of matrix operation between the equivalence relation matrix and the column matrix of fuzzy set membership degree is given. A matrix method for computing upper and lower approximation of fuzzy rough set model is proposed. The upper and lower approximation can be obtained from the calculation between the equivalence relation matrix and the column matrix of fuzzy set membership degree.A matrix method for computing upper and lower approximation of covering probability rough set model is given. The upper and lower approximation of unknown knowledge can be derived from the calculation between the covering matrix and the column matrix of concept. The combination between coverage and fuzzy rough set obtains four different covering fuzzy rough set model. The fourth model has different membership of the upper and lower approximation. Defining the coverage matrix fordifferent covering fuzzy rough set model and using matrix operations in the fuzzy rough set model, the matrix calculation for four covering fuzzy rough set model is respectively defined. The third model need to define the induced matrix about coverage in order to obtain approximation because it obtains degree membership of concept very complexly.Fourth model express upper and lower approximation of concept by the matrix calculation among covering matrix, the column matrix of concept’s membership degree and sectional matrix.Finally using the matrix for attribute reduction, the lower approximation is calculated by matrix method and the universe is divided by different attribute. Attribute reduction is obtained by delete redundant attributes.