Large group emergency decision-making with bi-directional trust in social networks: A probabilistic hesitant fuzzy integrated cloud approach

•A probabilistic hesitant fuzzy integrated cloud (PHFIC) model is proposed.•A new correlation coefficient between probabilistic hesitant fuzzy sets is put forward.•A bi-directional trust model through the social network and PHFIC is established.•Comparison and sensitivity analyses are performed to validate the superiority of our method. With the rapid development of society, the number of major emergencies in human society is gradually increasing. They are often accompanied by strong uncertainty and randomness, which makes traditional emergency decision-making methods unable to satisfy the practical needs. Hence, large group emergency decision-making (LGEDM) has gradually become an effective way to solve such problems. However, the existing decision-making methods usually employ a single model, which can't fully handle the uncertainty and randomness in LGEDM. In this paper, the probabilistic hesitant fuzzy set (PHFS) is used to adequately express the uncertainty of information, and the cloud model (CM) is served as a tool for dealing with the randomness of information. Therefore, a decision-making method based on PHFS and CM is proposed to tackle LGEDM. First, the probabilistic hesitant fuzzy integrated cloud (PHFIC) is raised, which can subjectively settle the uncertainty of LGEDM and objectively handle the randomness of LGEDM. Second, a hybrid correlation coefficient based on PHFS is advanced to reduce the complexity of LGEDM through hierarchical clustering. Third, a bi-directional trust model based on PHFIC is put forward to solve information conflict. Finally, an example is offered to prove the application of the proposed method. In addition, the sensitivity and comparison analyses show that the proposed method is able to deal with the uncertainty and randomness of information excellently.