Abstract The focus of this paper is on group decision making (GDM) problems with interval-valued Atanassov intuitionistic fuzzy preference relations (IV-AIFPRs). A new consistency index of an AIFPR is introduced to check the additive consistency degree of an AIFPR. Then, an additive consistency definition and an acceptable additive consistency definition of an IV-AIFPR are respectively defined by splitting an IV-AIFPR into two AIFPRs. For several IV-AIFPRs with unacceptably additive consistency, a goal program-based approach is proposed to improve their consistency simultaneously. Employing consistency degrees of individual IV-AIFPRs, decision makers’ (DMs’) weights are determined objectively and applied to integrate individual IV-AIFPRs into a collective one. Further, it is proved that the collective IV-AIFPR is acceptably additive consistent if all individual IV-AIFPRs are acceptably additive consistent. To derive priority weights of alternatives, an Atanassov intuitionistic fuzzy programming model is established and solved by three approaches considering DMs’ different risk attitudes. Thus, a novel method is put forward for GDM with IV-AIFPRs. A material selection example is analyzed to verify the effectiveness of the proposed method.