Three-way decision model with two types of classification errors

For an uncertain target set, three disjoint regions, i.e., positive, negative, and boundary regions, are established in a rough approximation space. To improve the fault-tolerance ability of the rough set model, a probabilistic rough set model with a pair of thresholds is proposed, and two types of classification errors are introduced from the viewpoint of probability and statistics. A decision-theoretic rough set model is proposed to minimize the decision risk, and a pair of thresholds of the probabilistic rough set model can be calculated by the given cost parameters. In this paper, first, two types of classification errors and two types of uncertain classifications are defined in the probabilistic rough set model. Then, by considering four cost parameters that characterize the cost of two types of classification errors and two types of uncertain classifications, a pair of thresholds of the probabilistic rough set model can again be obtained. Finally, with the increase in new attributes, the change regularities of the total cost with changing rough approximation spaces are discussed in detail, and experimental results show that the proposed model for three-way decision is reasonable and effective. These results further enrich three-way decision theory to effectively deal with uncertain classification problems. (C) 2017 Elsevier Inc. All rights reserved.