Hierarchies are extensively used in data warehouses, OLAP systems and more recently in data stream summarization systems.They indeed allow decision makers to consider information at multiple granularity levels and they enable efficient compression mechanisms. However, even if numerous models of hierarchies have been proposed, some hierarchies arising in real-world situations are still not manageable by the current systems. For instance, in medical applications, determining the normality of an arterial pressure measure is infeasible without considering the patient's characteristics (e.g. age). In this paper, we thus propose to model such context-dependent hierarchies by introducing personalized hierarchies. Firstly, we motivate this new category by presenting the lacks of existing approaches and we propose a conceptual model for modeling personalized hierarchies. Finally, a first logical model for handling such context-dependent hierarchies is proposed.