On fuzzy ideals in BCK/BCI-algebras

In the present paper we give a procedure by which we generate a fuzzy ideal (resp. closed fuzzy ideal) by a fuzzy set in a BCI-algebra. As applications we prove: The set of all the fuzzy ideals in a BCI-algebra forms a complete lattice (called fuzzy ideal lattice). The set of all the closed fuzzy ideals in a BCI-algebra is a modular sublattice of the fuzzy ideal lattice, but it is not distributive in general. For commutative BCK-algebras we establish the prime fuzzy ideal theorem. In particular, we give some characterizations of Noether BCK/BCI-algebras by fuzzy ideals.