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We give some propertes of fuzzy ideals and fuzzy biideals of a semigroup, and cbaracterize a regular semigroup, a semigroup that is a semilattice of left (right) simple semigroups, a semigroup that is a semilattice of left (right) groups, and a semigroup that is a semilattice of groups in terms of fuzzy left, right, and two-sided ideals and biideals.