In the previous work we accomplished the problem of defining fuzzy dependen
cy as well as projection and join operators which allow us to decompose a d
atabase in such a way that this process is fuzzy loss less. The definition
of rules-based fuzzy dependency did not satisfy the transitivity axiom, whi
ch is crucial to obtaining the completeness of the counterpart of Armstrong
axioms for fuzzy dependencies. In this paper we introduce an alternative d
efinition of dependency called restricted dependency, satisfying the transi
tivity property of inference. All the results obtained with the first defin
ition of dependency are also extended to this case. The price to pay for tr
ansitivity is a more restricted definition of fuzzy dependency. (C) 1999 El
sevier Science B.V. All rights reserved.