In this paper, we focus on the management of the user's context in the field of Fuzzy Database applications. Concretely, we propose an approach that uses fuzzy techniques to represent vague concepts with an adaptable semantics in order to meet user's preferences. We enhance previous work on the design and implementation of fuzzy databases, allowing a flexible use of different sets of linguistic labels for the same domain, which are transparently chosen according to user's context. This way, applications that operate on fuzzy databases get an additional piece of semantic power that makes an automatic customization in relation to user's preferences possible. This initial capability is proposed within a general architecture that aims at the management of the user context from a more general and interdisciplinary point of view. We complete our contribution with the description of a first proof of concept implementation of our proposal using the Oracle Object-Relational DBMS.