Multiple Attribute Decision Making (MADM) problems have received great attention from many researchers over the past decades. Many useful models and methods have been developed and applied in diverse fields. The objective of this paper is to integrate newly developed COmbinative Distance-based ASsessment (CODAS) method and Interval-Valued Intuitionistic Trapezoidal Fuzzy Set (IVITrFS) to cope with MADM problems. In the proposed method, IVITrFS is used considering membership and non-membership degrees of elements to handle more complex and flexible data than the ordinary fuzzy sets and their extensions. In addition, there has been no work extending CODAS method with IVITrFS to solve MADM problems in the literature. To illustrate applicability and effectiveness of the proposed method, a numerical example is employed for the selection of the most suitable investment project. A sensitivity analysis is applied to examine the stability and validity of the proposed approach. Then, the obtained results of the proposed method are compared with the existing methods to confirm the efficiency and reliability of the proposed method. Accordingly, the proposed IVITrFS-CODAS method is superior to CODAS, ordinary fuzzy CODAS and interval-valued Atanassov intuitionistic fuzzy CODAS (IVAIF-CODAS) methods since IVITrFS-CODAS deals with the hesitancy and fuzziness of human thinking better in decision-making process and provides larger domain for decision makers by assigning membership and non-membership scores in the interval between 0 (non-membership) and 1 (full membership). Finally, concluding remarks are presented at the end of the study.