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Intuitionistic multiplicative preference relation was recently introduced by Xia et al. to characterize the preference information given by a decision maker over a set of objects. All the elements of the intuitionistic multiplicative preference relation are the 2-tuples, which can simultaneously depict the degree that one object is prior to another, and the degree that the object is not prior to another. Each part of the 2-tuples takes its value from the closed interval [1/9, 9], and thus can describe the decision maker's preferences over objects more comprehensively than the traditional multiplicative preference relation. How to derive the priority weights of the objects from an intuitionistic multiplicative preference relation is an important research topic for decision making with intuitionistic multiplicative preference information. In this paper, we shall focus on solving this issue. We first define the concepts of expected intuitionistic multiplicative preference relation, left and right error matrices. Then based on the geometric aggregation operator and the error propagation formula, we derive the priority weight intervals from an intuitionistic multiplicative preference relation. After that, some approaches to decision making based on intuitionistic multiplicative preference relations are developed, and furthermore, two practical examples are given to illustrate our approaches.