Abstract
A fuzzy set is a concept theory that provide a solution of problem that cannot be explained by crisp set. Along with time, research of a fuzzy set are combined with algebra that produce fuzzy algebra. One of the research is a fuzzy subgroup and fuzzy level subset. The other research is an anti fuzzy subgroup that is inspired by a fuzzy subgroup. The purpose of this research is to write further study of anti fuzzy subgroup properties by induction of properties of fuzzy algebra such as fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. The research procedure is to study the basic concept of fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. Using that concept to proof the properties of the anti fuzzy subgroup. The conclusions are in the anti fuzzy subgroup, set with anti fuzzy subgroup is a subgroup of a group that can be applied to complement of and normal anti fuzzy subgroup closely related to anti fuzzy left coset, right coset, and middle coset.
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