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