Fuzzy functional dependencies and independencies in extended fuzzy relational database models

Abstract

In this paper we have considered data dependencies, more specifically (restricted) fuzzy functional dependencies, in the framework of extended fuzzy relational database model. A formal system is presented for the derivation of fuzzy functional dependencies, which is both sound and complete. The problem of lossless join decomposition is discussed in the framework of extended fuzzy relational model. Then we introduce a formal statement, of fuzzy functional independency, which expresses the fact that the corresponding restricted fuzzy functional dependency is not a legitimate constraint of the real world. A formal system is presented for the derivation of restricted fuzzy functional dependencies and independencies. The various problems such as the membership problem, the contradiction problem, and the problem of canonical represents are discussed. A cover, called minimal cover, of restricted fuzzy functional independencies is shown to be unique.