A Three-Way Decision Approach Combining Probabilistic and Decision-Theoretic Rough Set

The three-way decision (3WD) using probabilistic rough set (PRS) is constructed based on the probabilistic thresholds, and the 3WD using decision-theoretic rough set (DTRS) can utilize the decision cost information. They are both popular and effective decision-making methods. In the same problem, experts may provide different types of information about the decision rules. However, few works try to combine these two kinds of models and utilize both kinds of information. Therefore, in this paper, we propose a 3WD model combining PRS and DTRS, which integrates the probabilistic risk and the Bayesian risk in decision problems. To achieve that, based on the given probabilistic thresholds and decision rules, the 3WD with PRS is analyzed from the perspective of decision risk. Following that, the total risk of three decisions is computed. Then the best option for the instance is selected according to the Bayesian minimum risk rule. After the existence and uniqueness of the thresholds are analyzed, the explicit expressions are provided. Finally, illustration examples demonstrate the effectiveness of the proposed approach.