AbstractWith 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.KEYWORDS: Picture fuzzy setsoperation rulesmeasuresaggregation operatorsdecision-making methods Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe data that support the findings of this study are openly available in Web of Science data base.Additional informationFundingThis work is supported by the National Social Science Fund of China (No. 22BGL249).Notes on contributorsJuan Juan PengJuan 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 ChenXin 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 WangXiao 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 WangJian 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 LongQing 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 YinLv 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. 

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

The development of underground pumped storage plant using abandoned coal mine (UPSP-ACM) has a significance to abandoned coal mine resources utilization and energy storage industry. The article studies on site selection of UPSP-ACM and proposes a decision framework to determine the optimal location based on the theory of multi-criteria decision making (MCDM). Firstly, 15 evaluation criteria from resources and environment (R&E), investment and benefits (I&B), construction and technology (C&T), society and planning (S&P) four aspects are identified in the evaluation index system. Then, triangular intuitionistic fuzzy number (TIFN) is used to transform the information of qualitative index into the quantitative, and the game combined weight is used to analyze criteria’ importance. The result shows that average gross head with 0.149 weight is the most important among criteria, and the combined weight method can avoid the bias of single weight method. Further, TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) is used to rank the alternatives, which takes the decision maker's risk preference into account. Finally, the feasibility of decision framework testified through a case study in Shanxi province, and its stability and applicability are verified by sensitivity analysis and comparative analysis. Lastly, some suggestions to help the UPSP-ACM site selection are put forward based on the evaluation criteria. The research of article can provide a reference to person who is engaged in management decision research and UPSP-ACM site selection. • A site selection decision framework is proposed for underground pumped storage plant using abandoned coal mine. • Triangular intuitionistic fuzzy number is employed to describe the qualitative indexes. • BWM and entropy method are combined based on game theory to calculate the weight of criteria. • TODIM is used to determine the optimal result with the highest global dominance. • The practicability of decision framework is verified through a case study in Shanxi. 

Site selection for underground pumped storage plant using abandoned coal mine through a hybrid multi-criteria decision-making framework under the fuzzy environment: A case in China

Multi-attribute strategic weight manipulation with minimum adjustment trust relationship in social network group decision making

In this paper, we propose a new similarity measure (SM) between picture fuzzy sets (PFSs). The proposed SM between PFSs can overcome the drawbacks of the existing SMs between PFSs. We also propose a weight-determination approach based on the proposed SM between PFSs to determine attributes’ weights in picture fuzzy environments. We also propose a new multi-attribute decision-making (MADM) approach based on the proposed SM between PFSs and the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method for MADM with picture fuzzy information. The proposed MADM approach can overcome the shortcomings of the existing MADM approaches based on PFSs. It provides us a very useful approach for MADM in picture fuzzy settings. 

Multi-attribute decision-making based on similarity measure between picture fuzzy sets and the MARCOS method

Due to the urgent nature of emergency decision making, it is necessary to reach the consensus requirement quickly. Ordinal consensus measure explores the relation between the rankings and helps to intuitively know which alternative needs to be adjusted to accelerate the improvement of consensus. Moreover, decision makers (DMs) in the decision making problem are often connected through trust relationships which affect the DMs' judgments in the process of DMs' interaction. Therefore, this paper explores trust network-based group decision-making in which the consensus level is estimated by an ordinal consensus measure. We first focus on the supplementation of an incomplete trust network. One of the most common methods is to design the trust propagation operator, whereas the intensity of information propagation may be different in various scenarios. Therefore, considering the different numerical scale of the linguistic term set, a trust propagation operator with different intensity of trust propagation is designed to obtain the indirect trust relationship. In the process of supplementing the incomplete trust network, the contribution of DMs to propagating information is concerned, which can be described by the betweenness centrality, and the importance weights of DMs are determined by combining the betweenness centrality and trust in-degree. In the consensus reaching process, we first propose an improved ordinal consensus measure, which takes into account the consistency of orders of the same alternative in different rankings as well as the importance of positions of alternatives. Then, we design the identification rule and the feedback mechanism for those with low consensus levels. The identification rule is used to select the DMs which first few alternatives in the ranking are different with those in the ranking of group. And in the feedback mechanism, the referenced preference relation (FPR) obtained by the trust network is provided for the identified DMs. Afterwards, combining the referenced FPR, an optimization model is designed to give the adjustment opinion. Finally, a numerical example elaborates on the feasibility of the trust propagation operator and consensus model. The comparative analysis demonstrates the rationality and effectiveness of the proposed model. 

Consensus reaching process for group decision-making based on trust network and ordinal consensus measure

Picture fuzzy large-scale group decision-making in a trust- relationship-based social network environment

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Picture fuzzy large-scale group decision-making in a trust- relationship-based social network environment