Abstract As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.