In this paper, we have presented an uncertain database model based on possibility certainty. The idea is to associate every candidate value (or disjunction of such values) representing an ill-known piece of data with a degree expressing the extent to which the candidate value (or disjunction) is certain. We have extended relational algebra in this context and shown that the model constitutes a strong representation system for this set of operators. The only constraints concerns (i) the join which has to be based on an equality condition, (ii) the union, Cartesian product, and join operations which must take independent relations as arguments. An important result is that the data complexity of these operations is the same as in the classical database case.