The output of structure under fuzzy uncertainty can be classified into three cases, i.e., safety-failure case corresponding to that failure and safety both can occur in different membership levels, absolute failure case corresponding to that only failure can occur, and absolute safety case corresponding to that only safety can occur in any membership level. The existing fuzzy possibilistic safety degree measure models can only distinguish the structural safety degree in the safety-failure case but play no role in the absolute failure case and absolute safety case. Aiming at addressing this issue, a novel fuzzy possibilistic safety degree measure model is proposed. Before establishing the new fuzzy possibilistic safety degree measure model, a new value-interval ranking technique is first constructed. Then, the new safety possibility and failure possibility are estimated by synthesizing the information in the entire uncertain space based on the proposed value-interval ranking technique. The new fuzzy possibilistic safety degree measure model can distinguish the structural safety degree in all the three cases, and the results coincide with the human’s intuitive cognition. Several examples involving an engineering application with the finite element model are introduced to show the effectiveness of the established fuzzy possibilistic safety degree measure model.