In attempts to foster sustainability, where the effective use of natural resources and renewable energy is important, the problem of circular supplier selection (CSS) has become a central issue. To address this problem, for the first time, we propose a group decision model based on an integrated Analytic hierarchy process (AHP) and Complex proportional assessment (COPRAS) methodology in an Interval-valued intuitionistic fuzzy-sets (IVIFS) environment for dealing with uncertainty that shapes decision makers' judgements in solving the CSS problem. Based on experts' opinions and a review of relevant literature in the field, three main categories of criteria are developed: economic, social, and circular. The main contributions of the study are, first, to develop specific CSS criteria, and second, to propose a novel integrated method for the CSS process using IVIFS with AHP and COPRAS. After using the AHP method to calculate the weights of individual criteria, we employ the COPRAS method, in an IVIFS environment, to rank potential circular suppliers, testing the validity of the proposed method via a case study involving a multinational cement company from Turkey. We also conduct a one at-a-time sensitivity analysis to demonstrate the effect of criteria weights on the results of the proposed approach, and compare the results of the approach with those obtained using other multi-criteria decision-making methods.