Three-way group decisions with decision-theoretic rough sets

• GDM-based three-way decisions as an extension model of DTRSs is proposed.
• GDM provides a new semantic interpretation for three-way decisions.
• Our method explains the imprecise origin of the existing literatures.

On consideration of the effectiveness of group decision making (GDM) in practical complex decision problems, we introduce GDM into three-way decisions with decision-theoretic rough sets (DTRSs) and propose GDM-based three-way decisions. GDM-based three-way decisions extend the range of applications of three-way decisions with DTRSs and provide a novel interpretation of the determination of loss functions. Based on DTRSs, we firstly focus on analyzing the determination for the loss functions under the GDM environment. With the aid of the principle of justifiable granularity, we adopt the important and majority suggestions of experts to measure each loss function, which supports a coherent way of designing information granules in presence of numerics. In this case, the loss functions are determined in the form of interval-valued information granule. By using the interval comparison method, we further deduce the three-way decisions and design a corresponding decision procedure of GDM-based three-way decisions. Then, an example of strategy supply selection is given to elaborate the GDM-based three-way decisions. Finally, we validate the performance of our proposed method by experimental analysis.