Research of interval reduction in variable precision rough set

The essence of reduction is to find a minimal attribute subset having the same classification ability without inducing new inconsistency with a given decision information system. In variable precision rough set, interval reduction based on beta-classification quality leads to several kinds of reduction anomalies. In this study, the authors define interval reduction based on beta-lower approximation distribution to avoid all kinds of reduction anomalies. The merger of condition classes is discussed and a method is presented to get interval reduction based on the ordered discernibility matrix of condition classes. The property of interval core attribute which is the most important attribute on the given beta-interval is also discussed and a method is given to calculate core attribute on beta-lower approximation distribution hierarchy. In addition, the core attribute set is usually used as the original subset in the heuristic algorithm for attribute reduction.