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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 …