With the advent of information age, supplier selection has attracted researchers' attention in the field of supply chain management. Optimal supplier selection meets the competitiveness of industries and satisfaction of customers in the supply chain management. However, considering sustainable factors including environmental and social parameters, alongside customers' expectations are the main challenge of supplier selection. Moreover, incomplete and hesitation among experts' judgment result in uncertainty that leads the more complex assessment of criteria. In this paper, an innovative multi -criteria decision making method was developed to address supplier selection process and supplier order allocation based on customers' expectations with respect to the sustainable primers. The proposed method was based on fuzzy Combinative Distance-based Assessment (CODAS) extended with Interval-Valued Intuitionistic Fuzzy ( IVIF ) for multi -criteria sustainable supplier selection. The proposed model was combined with hesitation linguistic set to provide two goals including a: dealing with experts' hesitation as well as imprecise and vague of decision makers' knowledge in order to express assessment values. b: coping with missing or nonexistence of attribute assessment values. The proposed method was performed on a steel mill as a case study to illustrate the effectiveness of decision process on four suppliers in detail. The results showed that the presented model could consider conflicting parameters and enhance high order imprecision and uncertainty.