This paper considers relational databases containing uncertain attribute values when some knowledge is available about themore or less certain value (or disjunction of values) that a given attribute in a tuplemaytake. We propose a possibility-theory-based model suited to this context and extend the operators of relational algebra to handle such relations in a "compact," thus efficient, way. It is shown that the model is a 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.