In the context of a microbiological application, our study proposes to extend the Conceptual Graph Model in order to allow one: (i) to represent imprecise data and queries that include preferences, by using fuzzy sets (from fuzzy set theory) in concept vertices, in order to describe either an imprecise concept type or an imprecise referent; (ii) to query a conceptual graph that may include imprecise data (factual graph) using a conceptual graph that may include preferences (query graph). This is performed in two steps: firstly by extending the projection operation to fuzzy concepts, secondly by defining a comparison operation characterised by two matching degrees: the possibility degree of matching and the necessity degree of matching between two graphs, and particularly between a query graph and a factual graph.