This paper focuses on one of the fundamental design issues in fuzzy database modeling, namely, the dependency-preserving decomposition. In a fuzzy relational data model where imprecision is reflected by possibility distributions for attribute values as well as by closeness relations for domain elements, a ''poor'' model design can be remedied, in many cases, by decomposing relation schemes in order to eliminate/reduce data redundancy and update anomalies. On the other hand, the decomposition should guarantee that the semantic knowledge and integrity constraints expressed by fuzzy functional dependency (FFD) are satisfactorily preserved by the resultant relation schemes. Based on the concept of FFD transitive closure, an algorithm has been developed to test whether a given decomposition is dependency-preserving with respect to a given set of FFDs. Finally, two special FFD sets, one composed of a X(1)-to-X(1) FFD loop and the other composed of a X(1)-X(m) FFD and a X(1)-to-X(m) FFD chain, are investigated.