Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems: Survey and Challenges

Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on effective, cognitive, and social processes employed by humans for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions.