To cope with the strategic location and configuration problem of multi-stage closed-loop supply chain network design under low-carbon environment, a multi-objective robust fuzzy optimization model is developed by considering the fuzzy parameters and multiple product flows. This model aims to minimize the total costs and total carbon emissions of the supply chain network. It also regards the lowest conservatism level of the chance constraints as decision variables, and achieves an effective balance among the expected value of the objective function, optimality robustness and feasibility robustness. Finally, an interactive $\varepsilon-$constraint fuzzy solution approach based on the necessity measure is proposed, and a numerical example is given to illustrate the effectiveness, and feasibility of the proposed model and algorithm.