Generation of Reducts and Threshold Functions Using Discernibility and Indiscernibility Matrices for Classification

Dimension reduction of data is an important issue in the data processing and it is needed for the analysis of higher dimensional data in the application domain. Reduct in the rough set is a minimal subset of features, which has the same discernible power as the entire features in the higher dimensional scheme. In this paper, generations of reducts and threshold functions are developed for the classification system. The reduct followed by the nearest neighbor method or threshold functions is useful for the reduct classification system. For the classification, a nearest neighbor relation with minimal distance proposed here has a fundamental information for classification. Then, the nearest neighbor relation plays a fundamental role on the discernibility and in discernibility matrices, in which the indiscernibility matrix is proposed here to test the sufficient condition for reduct and threshold function. Then, generation methods for the reducts and threshold functions based on the nearest neighbor relation are proposed here using Boolean operations on the discernibility and the indiscernibility matrices.