Abstract: Rough set theory can be applied to rule induction. There are two different types of classification rules, positive and boundary rules, which leading to different decisions and consequences. They can be distinguished from the syntax measures and semantic measures. Both the two can be interpreted by a probabilistic extension of the Pawlak rough set model. Attribute reduction is an important concept of rough set theory. This paper addresses attribute reduction in decision-theoretic rough set models regarding the classification properties of decision-monotonicity and provides a positive-based Veduction model in attribute reduction and its analysis.
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Key words: decision-theoretic rough set, attribute reduction, loss function