Disruption risks exacerbate the complexity of low-carbon supply chain network design in an uncertain supply chain environment. Considering the low frequency and non-repeatability of these disruption events makes it impossible to collect data to obtain their probabilities. In this study, supply disruptions were regarded as uncertain events; supply chain uncertain disruption risk is defined and quantified based on the uncertainty theory, in which uncertain disruptions are characterized by the belief degree on account of expert estimation with duality, i.e., symmetry. Optimization models were constructed with the objective of minimizing expected carbon emissions and costs, which optimizes the selection of suppliers with uncertain disruptions, and the assignment of manufacturers and customers. The properties of the model were analyzed, and the models were solved separately using different methods according to different decision criteria. Finally, the validity of the proposed models and algorithm were verified using a real case study of a glass manufacturing company. The findings exhibit promising insights for designing a sustainable and resilient supply chain network in an uncertain environment.