Abstract:

With the increasing complexity of decision-making problems and the increasing scale of decision-making groups， how to aggregate large group decision-making information to obtain satisfactory decision-making results is a key step and an important part of multi-attribute large group decision-making problems. However， in the previous research on multi-attribute large group decision-making methods， most of them usually assume that decision makers are independent of each other， and rarely consider the social network relationship among decision makers. At the same time， most of the existing multi-attribute large group decision-making methods based on social trust network have not considered the realistic situation that decision makers belong to multiple groups or decision makers are isolated nodes. In order to solve these problems， in this paper， a new multi-attribute large group decision making method based three-dimensional probabilistic linguistic density operator is proposed. First， for the situation that decision makers belong to multiple groups or have isolated nodes in decision making， the improved method of social network analysis is used to make a proper cluster for large group decision makers based on the social trust network relationship among decision makers. Then， the weight of decision makers can be obtained by measuring the similarity of preference information of decision makers in the sub-groups， and the comprehensive density weight of sub-groups can be obtained by the linear combination of the vectors of centrality， trust and the number of decision makers in the sub-groups. Finally， the three-dimensional probabilistic linguistic density operator is defined， which is used to aggregate large group probabilistic linguistic evaluation information.Through an emergency management decision-making case， the proposed method is effectively applied. The case shows that the decision-making method is reasonable and reliable as it not only can deal with the social trust network relationship among large group decision makers， but also can effectively aggregate the probabilistic linguistic information of large group decision making. On this basis， in order to illustrate the advantages of this method， the group decision-making methods in previous studies are introduced to conduct the method comparisons. The results show that the decision-making method based on three-dimensional probabilistic linguistic density operator enhances the flexibility and stability of large group decision-making expert clustering， and improves the consensus level of large group decision-making.

Key words: social network analysis, multiple attribute decision making, large group decision making, density operator, probabilistic language