The selection of a proper international freight transport route is one of the crucial tasks for decision-makers since it can affect costs, efficiency, and transportation performance. Besides, the selection of suitable and appropriate freight routes can also reduce external costs of transportation such as emissions, noise, traffic congestions, accidents, and so on. Route selection in international transportation is a complicated decision-making problem as many conflicting factors and criteria affect the assessment process. It has been observed that there is no mathematical model and methodological frame used for solving these selection problems, and decision-makers make decisions on this issue based on their own experiences and verbal judgments in the research process. Therefore, a methodological frame is required to make rational, realistic, and optimal decisions on route selection. From this perspective, the current paper proposes using the IVAIF CODAS, an extended version of the traditional CODAS techniques, and using the Atanassov interval-valued intuitionistic fuzzy sets (IVAIFS) for processing better the existing uncertainties. The proposed model is applied to solve the route selection, a real-life decision-making problem encountered in international transportation between EU countries and Turkey. According to the results of the analysis, option A6 (i.e., Route -6 (Bursa - Istanbul - Pendik-Trieste (Ro-Ro) - Austria - Frankfurt / Germany) has been determined as the best alternative. These obtained results have been approved by a comprehensive sensitivity analysis performed by using different MCDM techniques based on interval-valued intuitionistic fuzzy sets. Hence, it can be accepted that the proposed model is an applicable, robust, and powerful mathematical tool; also, it can provide very reliable, accurate, and reasonable results. As a result, the proposed model can provide a more flexible and effective decision-making environment as well as it can provide valuable advantages to the logistics and transport companies for carrying out practical, productive, and lower costly logistics operations.