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Abstract
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.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The data that support the findings of this study are openly available in Web of Science data base.
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Notes on contributors
Juan Juan Peng
Juan Juan Peng received her Ph.D. from Central South University, Changsha, China. She is currently an associate professor in the School of Information, Zhejiang University of Finance and Economics, Hangzhou, China. Her research interests lie in the field of decision-making theories and methods, matching theories and methods, data analysis and mining.
Xin Ge Chen
Xin Ge Chen received her bachelor’s degree from Chongqing Normal University, Chongqing, China. She is currently a postgraduate student in the School of Information, Zhejiang University of Finance and Economics, Hangzhou, China. Her research interest includes decision-making theories and methods.
Xiao Kang Wang
Xiao Kang Wang received the Ph.D. degree in Management Science and Engineering from Central South University, Changsha, China, in 2023. He is currently a lecturer in the School of Business, Shenzhen University, Shenzhen, China. His current research interests include decision-making theory and application, risk management and control, and information management.
Jian Qiang Wang
Jian Qiang Wang received the Ph.D. degree in Management Science and Engineering from Central South University, Changsha, China, in 2005. He is currently a Professor in School of Business, Central South University, Changsha, China. His current research interests include decision-making theory and application, risk management and control, and information management.
Qing Qi Long
Qing Qi Long received his Ph.D. from Tongji University, Shanghai, China. He is currently a professor in the School of Information, Zhejiang University of Finance and Economics, Hangzhou, China. His current research interests include management system computing and simulation, data-driven decision-making optimisation.
Lv Jiang Yin
Lv Jiang Yin received his Ph.D. from Huazhong University of Science and Technology, Wuhan, China. He is currently a professor in the School of Economics and Management, Hubei University of Automotive Technology, Shiyan, China. His research interests include operations research optimisation.