Abstract: The definition of anti-fuzzy semigroups and anti-fuzzy semigroups complement is introduced,and the sufficient and necessary condition of the existence of the anti-fuzzy semigroups complement is obtained.Based on the definition of value-keeping fuzzy mappings in semigroups,the paper proves invariance of the homomorphism of anti-fuzzy semigroups and normal anti-fuzzy semigroups.Furthermore,the definition of anti-fuzzy (left,right,bilateral or within) ideals is introduced,and the sufficient and necessary condition of the existence of the anti-fuzzy (left,right,bilateral or within) ideal is achieved.Finally,the paper discusses invariance of the homomorphism of anti-fuzzy (left,right,bilateral or within) ideal under the condition of the homomorphic mapping.