Most of the previous studies on the user preferences assume that there is a personal transitive preference ranking of the consumable media like images. For example, the transitivity of preferences is one of the most important assumptions in the recommender system research. However, the intransitive relations have also been widely observed, such as the win/loss relations in online video games, in sport matches, and even in rock-paper-scissors games. It is also found that different subjects demonstrate the personalized intransitive preferences in the pairwise comparisons between the applicants for college admission. Since the intransitivity of preferences on images has barely been studied before and has a large impact on the research of personalized image search and recommendation, it is necessary to propose a novel method to predict the personalized intransitive preferences of images. In this paper, we propose the novel Multi-Criterion preference (MuCri) models to predict the intransitive relations in the image preferences. The MuCri models utilize different kinds of image content features as well as the latent features of users and images. Meanwhile, a new data set is constructed in this paper, in order to evaluate the performance of the MuCri models. The experimental evaluation shows that the MuCri models outperform all the baselines. Due to the interdisciplinary nature of this topic, we believe it would widely attract the attention of researchers in the image processing community as well as in other communities, such as machine learning, multimedia, and recommender system.