By introducing the misclassification and delayed decision costs into the probabilistic approximations of the target, the model of decision-theoretic rough set is then sensitive to cost. However, traditional decision-theoretic rough set is proposed based on one and only one cost matrix, such model does not take the characteristics of multiplicity and variability of cost into consideration. To fill this gap, a multicost strategy is developed for decision-theoretic rough set. Firstly, from the viewpoint of the voting fusion mechanism, a parameterized decision-theoretic rough set is proposed. Secondly, based on the new model, the smallest possible cost and the largest possible cost are calculated in decision systems. Finally, both the decision-monotocity and cost criteria are introduced into the attribute reductions. The heuristic algorithm is used to compute decision-monotonicity reduct while the genetic algorithm is used to compute the smallest and the largest possible cost reducts. Experimental results on eight UCI data sets tell us: 1. compared with the raw data, decision-monotocity reduct can generate greater lower approximations and more decision rules; 2. the smallest possible cost reduct is much better than decision-monotocity reduct for obtaining smaller costs and more decision rules. This study suggests new research trends concerning decision-theoretic rough set theory. 
Decision-theoretic rough set: A multicost strategy