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The intuitionistic multiplicative preference relation (IMPR), which takes into account both the ratio degree to which an alternative is preferred to another and the ratio degree to which an alternative is non-preferred to another, is a useful tool for decision makers to elicit their preference information using Saaty’s 1–9 scale. In this paper, we focus on group decision making with IMPRs. First, we analyze the flaws of the consistency definition of an IMPR in previous work and then propose a new definition to overcome the flaws. On this basis, a linear programming-based algorithm is developed to check and improve the consistency of an IMPR. Second, we discuss the relationships between an IMPR and a normalized intuitionistic multiplicative weight vector and develop two approaches to group decision making based on complete and incomplete IMPRs, respectively. Based on the proposed algorithm and approaches, a …