Multi-attribute group emergency decision making (MAGEDM) has become a valuable research topic in the last few years due to its effectiveness and reliability in dealing with real-world emergency events (EEs). Dynamic evolution and uncertain information are remarkable features of EEs. The former means that information related to EEs is usually changing with time and the development of EEs. To make an effective and appropriate decision, such an important feature should be addressed during the emergency decision process; however, it has not yet been discussed in current MAGEDM problems. Uncertain information is a distinct feature of EEs, particularly in their early stage; hence, experts involved in a MAGEDM problem might hesitate when they provide their assessments on different alternatives concerning different criteria. Their hesitancy is a practical and inevitable issue, which plays an important role in dealing with EEs successfully, and should be also considered in real world MAGEDM problems. Nevertheless, it has been neglected in existing MAGEDM approaches. To manage such limitations, this study intends to propose a novel MAGEDM method that deals with not only the dynamic evolution of MAGEDM problems, but also takes into account uncertain information, including experts' hesitation. A case study is provided and comparisons with current approaches and related discussions are presented to illustrate the feasibility and validity of the proposed method.