In order to capture/model uncertainty associated with imprecision or vagueness, a decision maker may express her/his judgments in terms of intuitionistic multiplicative preference relation (IMPR). Two important research topics with this regard are studied in the paper: 1) checking consistency of IMPR and 2) generating weights on the basis of this relation. A new definition of consistent IMPR is proposed. In light of this new definition, the properties of consistent IMPR are studied in detail. A transformation formula is proposed to construct a consistent IMPR from a given normalized intuitionistic fuzzy weight vector. By minimizing the differences between the constructed consistent IMPR and the given IMPR, some fractional programming models are developed to derive the intuitionistic fuzzy weight vector. Moreover, the models are also extended to group decision making. Finally, two numerical examples are provided to illustrate the effectiveness and practical relevance of the proposed models.