Cost-sensitive rough set approach

We consider test cost and decision cost simultaneously.Cost-sensitive rough set was proposed and explored.Attribute reductions based on three different criteria were investigated. Cost sensitivity is an important problem, which has been addressed by many researchers around the world. As far as cost sensitivity in the rough set theory is concerned, two types of important costs have been seriously considered. On the one hand, the decision cost has been introduced into the modeling of decision-theoretic rough set. On the other hand, the test cost has been taken into account in attribute reduction. However, few researchers pay attention to the construction of rough set model with test cost and decision cost simultaneously. To fill such a gap, a new cost-sensitive rough set approach is proposed, in which the information granules are sensitive to test costs and approximations are sensitive to decision costs, respectively. Furthermore, with respect to different criteria of positive region preservation, decision-monotonicity and cost decrease, three heuristic algorithms are designed to compute reducts, respectively. The comparisons among these three algorithms show us: (1) positive region preservation based algorithm can keep the decision rules supported by lower approximation region unchanged; (2) decision-monotonicity based heuristic algorithm can obtain a reduct with more positive decision rules and higher classification accuracy; (3) cost minimum based algorithm can generate a reduct with minor cost. This study suggests potential application areas and new research trends concerning rough set theory.