The competition in the new energy vehicle industry has intensified with the rapid development of the industry. In order to create innovative products, many businesses are now seeking cooperation with their supply chain members. Previous research on the new energy vehicle supply chain has mainly focused on government policies, supply chain retailers and with consumer gaming issues. This manuscript examines the problem of cooperation decisions between members of the new energy vehicle supply chain, namely a battery manufacturer and vehicle producer. The benefits of the two members are analyzed by constructing two models, one with non-incentives and the other with government incentives. The model uses the triangular fuzzy number (TFN) instead of parameters in numerical calculations, taking complete account of the influence of uncertain environmental factors and using the triangular structured element method. The numerical examples result that government incentives positively promote cooperation between the two players, but the incentives should be as equal as possible. Finally, we aim to encourage supply chain members to cooperate and promote the development of the new energy vehicle industry. This study has positive implications for future supply chain member cooperation issues.