A Note on Attribute Reduction in the Decision-Theoretic Rough Set Model

This paper studies the definitions of attribute reduction in the decision-theoretic rough set model, which focuses on the probabilistic regions that induce different types of decision rules and support different types of decision making successively. We consider two groups of studies on attribute reduction. Attribute reduction can be interpreted based on either decision preservation or region preservation. According to the fact that probabilistic regions are non-monotonic with respect to set inclusion of attributes, attribute reduction for region preservation is different from the classical interpretation of reducts for decision preservation. Specifically, the problem of attribute reduction for decision preservation is a decision problem, while for region preservation is an optimization problem.