Abstract
We introduce the concept of anti fuzzy subgroups of groups, lower level subset of a fuzzy subset, lower level subgroups and prove some results on these. We show that a fuzzy subset of a group is a fuzzy subgroup iff the complement of this fuzzy subset is anti fuzzy subgroup. We fuzzify lower level subsets and prove that if a fuzzy set is an anti fuzzy subgroup then the fuzzifications of its lower level subsets are also anti fuzzy subgroups.
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