This study explores a foundational logistics center location and allocation problem in a three-stage logistics network that consists of suppliers, logistics centers, and customers. In this study, the environmental sustainability of the logistics network is improved by optimizing the carbon dioxide emissions of the logistics network based on multi-objective optimization and carbon tax regulation. Mixed uncertainties in the planning stage, including the supply capacities of suppliers, operation capacities of logistics centers, and demands of customers, are modeled using triangular fuzzy numbers based on the fuzzy set theory to order to enhance the reliability of the logistics center location and allocation planning. To solve the green logistics center location and allocation problem under mixed uncertainties, we establish two fuzzy mixed integer linear programming models. The fuzzy credibilistic chance-constrained programming is then adopted to obtain the crisp and linear reformulations of the fuzzy programming models. A numerical case is given to verify the feasibility of the proposed methods, in which the performance of carbon tax regulation in reducing carbon dioxide emissions is then tested based on the benchmark provided by the multi-objective optimization. Lastly, sensitivity analysis and fuzzy simulation are utilized to reveal the effect of the mixed uncertainties on the logistics location and allocation planning and further determine the best confidence level in the fuzzy chance constraints to provide decision makers with a crisp plan.