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 φφ-fuzzy ideals of a fuzzy semigroup X is a complete sublattice of the lattice of all fuzzy sets in X   when φφ is an infinitely ∨∨-distributive weak pseudo-t-norm on L  . A definition of φφ-semiprime fuzzy ideal of a fuzzy semigroup is given. A description of all φφ-semigroups, in which every φφ-fuzzy ideal is φφ-semiprime, is obtained.