Fuzzy ideals and semiprime fuzzy ideals in semigroups

In this paper, we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup. The equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained. We show that the lattice of all image-fuzzy ideals of a fuzzy semigroup X is a complete sublattice of the lattice of all fuzzy sets in X when image is an infinitely image-distributive weak pseudo-t-norm on L. A definition of image-semiprime fuzzy ideal of a fuzzy semigroup is given. A description of all image-semigroups, in which every image-fuzzy ideal is image-semiprime, is obtained.