Variable Precision Rough Set Model for Incomplete Information Systems and Its Β-reducts

As the original rough set model is quite sensitive to noisy data, Ziarko proposed the variable precision rough set (VPRS) model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. In this paper, the variable precision rough set model for an incomplete information system is proposed by combining the VPRS model and incomplete information system, and the β-lower and β-upper approximations are defined. Considering that classical VPRS model lacks a feasible method to determine the precision parameter β when calculating the β-reducts, we present an approach to determine the parameter β. Then, by calculating discernibility matrix and discernibility functions based on β-lower approximation, the β-reducts and the generalized decision rules are obtained. Finally, a concrete example is given to explain the validity and practicability of β-reducts which is proposed in this paper.