Multi-Criteria Recommender Systems (MCRSs) have been developed to improve the accuracy of single-criterion rating-based recommender systems that could not express and reflect users’ fine-grained rating behaviors. In most MCRSs, new users are asked to express their preferences on multi-criteria of items, to address the cold-start problem. However, some of the users’ preferences collected are usually not complete due to users’ cognitive limitation and/or unfamiliarity on item domains, which is called ‘partial preferences’. The fundamental challenge and then negatively affects to accurately recommend items according to users’ preferences through MCRSs. In this paper, we propose a Hypothetical Tensor Model (HTM) to leverage auxiliary data complemented through three intuitive rules dealing with user’s unfamiliarity. First, we find four patterns of partial preferences that are caused by users’ unfamiliarity. And then the rules are defined by considering relationships between multi-criteria. Lastly, complemented preferences are modeled by a tensor to maintain an inherent structure of and correlations between the multi-criteria. Experiments on a TripAdvisor dataset showed that HTM improves MSE performances from 40 to 47% by comparing with other baseline methods. In particular, effectivenesses of each rule regarding multi-criteria on HTM are clearly revealed.