Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets

Three-way decisions with decision-theoretic rough sets (DTRSs) provide a new methodology to confront risk decision problems. The risk is associated with the loss function of DTRSs. Under the intuitionistic fuzzy environment, we combine the loss functions of DTRSs with intuitionistic fuzzy sets (IFSs). Considering the new evaluation format of loss function with intuitionistic fuzzy numbers (IFNs), we propose a naive model of intuitionistic fuzzy decision-theoretic rough sets (IFDTRSs) and elaborate its relevant properties in advance. At this point, a critical issue is the determination of three-way decisions. In the frame of IFDTRSs, we then explore deriving three-way decisions for single-period decision making. Based on the positive and negative characteristics of IFNs, we design three strategies to address IFNs and derive corresponding three-way decisions. Meanwhile, we compare the three strategies and summarize their own applicabilities. In order to accommodate multi-period scenarios, we further extend IFDTRSs to the multi-period situation. With the aid of the results of the single period decision making, we analyze three aggregation operations of IFDTRSs for multi-period information, which are DIFWA, DIFPA and DIFOA, respectively. By comparing these operations, an algorithm for deriving three-way decisions in multi-period decision making is designed. These results help us to make a reasonable decision in the intuitionistic fuzzy environment. Finally, an example is presented to elaborate on three-way decisions with IFDTRSs.