In this paper, we consider relational databases containing uncertain attribute values, in the situation where some knowledge is available about the more or less certain value (or disjunction of values) that a given attribute in a tuple can take. We propose a possibility-theory-based model suited to this context and extend the operators of relational algebra in order to handle such relations in a “compact” thus efficient way. It is shown that the proposed model is a strong representation system for the whole relational algebra. An important result is that the data complexity associated with the extended operators in this context is the same as in the classical database case, which makes the approach highly scalable.