Generation of reducts and threshold functions using discernibility and indiscerniblity matrices

Dimension reduction of data is an important issue in the data processing and iti is needed for the analysis of higher dimensional data in the application domain. Rough set is fundamental and useful to reduce higher dimensional data to lower one. 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. The nearest neighbor relation with minimal distance proposed here has a fundamental information for classification. The nearest neighbor relation plays a fundamental role for generation of reducts and threshold functions using the Boolean reasoning 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, genetation 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.