Supplier selection can be considered as a complicated multi criteria decision-making problem.In this paper the problem of supplier selection is studied in the presence of conflicting evaluations and insufficient information about the criteria and different attitudes of decision makers towards the risk. Most of fuzzy approaches used in multi-criteria group decision making (MCGDM) are non-intuitionistic, which significantly restricts their application areas. Because of considering belongingness and non-belongingness of the issue in a same time, intuitionistic fuzzy sets can better encounter with a real supplier selection problem. Also to deal with different attitudes of decision makers toward the risk, the proposed approach in this paper employs a new decision function to participate this factor in decision process. In order to integrate fuzzy information, interval-valued intuitionistic fuzzy ordered weighted aggregation (IIFOWA) is applied to aggregate the obtained preferences. The influence of unfair arguments in final results can be reduced by assigning low weights to the “optimistic” or “pessimistic” discretions. Ranking process is based on the two indices, weighted score function and weighted accuracy function. To demonstrate the efficiency of the proposed approach, it is implemented to  supplier selection in a project-based company.