Fractionary fuzzy ideals and Dedekind domains

We show that a finite-valued fractionary fuzzy ideal of R with invertible level ideals has a finite minimal generating set (as a fuzzy R-submodule). We also characterize Dedekind domains in terms of the factorization of fuzzy ideals as products of prime fuzzy ideals and also in terms of the invertibility of certain fractionary fuzzy ideals. We also examine the factorization of fractionary fuzzy ideals.