Over the past decades, multimodal transportation has played a crucial role in modern logistics and transportation systems due to its high capacity and low cost. However, multimodal transportation, which is mainly driven by fossil fuels, potentially contributes to significant carbon emissions. In the context of global sustainable development, reducing carbon emissions from the transportation sector has far-reaching implications for supporting society-wide carbon neutrality. In this paper, we have developed for the first time a many-objective multimodal transportation route optimization (MTRO) model that simultaneously considers economic cost, carbon emission cost, time cost, and customer satisfaction, and solve it using the Non-dominated Sorting Genetic Algorithm Version III (NSGAIII). Second, to further improve the convergence performance, we introduce a fuzzy decision variable framework to improve the NSGAIII algorithm. This framework can reduce the search range of optimization algorithm in the decision space and make it converge better. Finally, we conducted a large number of simulation experiments on test problems to verify the applicability and superiority of the improved algorithm, and applied it to MTRO problems under uncertain demand. This work fills the research gap for MTRO problems and provides guidance for relevant departments to develop transportation and decarbonization plans.