Abstract: The join dependency provides the basis for obtaining
lossless join decomposition in a classical relational schema. The
existence of Join dependency shows that that the tables always
represent the correct data after being joined. Since the classical
relational databases cannot handle imprecise data, they were
extended to fuzzy relational databases so that uncertain, ambiguous,
imprecise and partially known information can also be stored in
databases in a formal way. However like classical databases, the
fuzzy relational databases also undergoes decomposition during
normalization, the issue of joining the decomposed fuzzy relations
remains intact. Our effort in the present paper is to emphasize on this
issue. In this paper we define fuzzy join dependency in the
framework of type-1 fuzzy relational databases & type-2 fuzzy
relational databases using the concept of fuzzy equality which is
defined using fuzzy functions. We use the fuzzy equi-join operator
for computing the fuzzy equality of two attribute values. We also
discuss the dependency preservation property on execution of this
fuzzy equi- join and derive the necessary condition for the fuzzy
functional dependencies to be preserved on joining the decomposed
fuzzy relations. We also derive the conditions for fuzzy join
dependency to exist in context of both type-1 and type-2 fuzzy
relational databases. We find that unlike the classical relational
databases even the existence of a trivial join dependency does not
ensure lossless join decomposition in type-2 fuzzy relational
databases. Finally we derive the conditions for the fuzzy equality to
be non zero and the qualification of an attribute for fuzzy key.