Evaluating and selecting suitable low-carbon suppliers is one of the most disputed topics in different industries. Some studies have more specifically investigated the role of sustainable low-carbon suppliers in the maritime sector. In general, sustainability is recognized as a vital philosophy for many industrial sectors since it enhances environmental protection and raises people's and organizations' awareness about social obligations. Therefore, choosing low-carbon suppliers based on the sustainability perspective is important for firms and organizations in order to effectively promote sustainable supplier chain management (SSCM). The present study develops a new fuzzy decision-making approach to rank and evaluate low-carbon, sustainable suppliers (LCSS) through the integration of the Combinative Distance-Based Assessment (CODAS) framework and intuitionistic fuzzy sets (IFSs), which results in a new approach called intuitionistic fuzzy CODAS (IF-CODAS). The paper is aimed at making a decision on the IFSs context by considering the decision makers' hesitancy based on both Hamming and Euclidean distances in accordance with the anti-ideal point. To evaluate the weights of the criteria, a new discrimination measure is developed. To show the practicality of the proposed approach, a case study for the assessment of low carbon sustainable suppliers is presented. To validate the developed approach, comparative research and sensitivity analysis were conducted in this study. The evaluation results showed that the fourth low-carbon sustainable supplier with a maximum assessment score degree (0.4747) using the proposed method was found the best option for selecting LCSS based on the sustainability perspective. Furthermore, the sensitivity analysis was made to observe the difference of alternative ranking when the importance values of criteria weights change.