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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.
We give some properties of fuzzy quasi-ideals of a semigroup, and characterize a completely regular semigroup and a semigroup that is a semilattice of groups in terms of fuzzy semiprime quasi-ideals.
In this paper we introduce the concept of fuzzy generalized bi-ideal of a Γsemigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γsemigroup and characterize regular Γ-semigroups in terms of fuzzy generalized bi-ideals. AMS Mathematics Subject Classification(2000): 08A72, 20M12, 3F55
A complete description of the congruences on a group in terms of its normal,subgroups can be seen in papers by A. Rosenfeld and W. J. Howie. In this paper, we shall introduce the concept of fuzzy congruences on a groupoid and a group, and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups.