Abstract
In this paper, we redefine the definition of a fuzzy HX group and define a new algebraic structure of Q-fuzzy HX group and anti Q-fuzzy HX subgroup and some related properties are ivestigated. We establish the relation between Q-fuzzy HX group and anti Q-fuzzy HX group of a HX group . The purpose of this study is to implement the fuzzy set theory and group theory in anti Q-fuzzy HX subgroups. Characterizations of lower level subsets of an anti Q-fuzzy HX subgroup of a HX group are given.
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