An extended relational model without semantic ambiguity, called a semantic-ambiguity-free relational model, is proposed using fuzzy sets and the theory of possibility. The model features every attribute having a membership attribute whose value consists of a pair of values based on necessity and possibility measures. The membership attribute value of an attribute in a base relation is the degree to which the attribute value is compatible with integrity constraints imposed on the base relation. This clarifies the source of the membership attribute value. The model has no semantic ambiguity for interpreting membership attribute values, unlike models consisting of relations with membership attribute values attached to tuple values. We show the formulation of 8 operations – union, intersection, difference, Cartesian product, projection, join, selection, and quotient – consisting of relational algebra proposed by Codd for query processing. This approach shows how to prevent users from misinterpreting tuples in databases allowing imperfect information.