Picture fuzzy decision-making theories and methodologies: a systematic review

With the generalisation of intuitionistic fuzzy sets (IFSs), picture fuzzy sets (PFSs) have been developed based on membership, neutral membership, and non-membership degrees. Compared with IFSs, PFSs can more accurately represent uncertainty in real-world decision-making problems. Recently, the research on decision-making theories and methods under picture fuzzy environments has been rapidly developing. Therefore, this manuscript presents a systematic review of picture fuzzy decision-making theories and methods, including the context in which this field was developed, the current status and advancements of this field, and the main research results obtained with the picture fuzzy information. First, this review introduces the development process of PFSs and the current status of corresponding theories. Next, the basic theories based on PFSs, including operations rules, measures, and aggregation operators are introduced. Afterward, this review summarises the current research on multi-criteria decision-making (MCDM), multi-criteria group decision-making (MCGDM), and large-scale group decision-making (LSGDM) methods with picture fuzzy information. Finally, future research directions of picture fuzzy decision-making theories and methodologies are discussed.