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Abstract
In this paper first we use the notion of Sperner family and we introduce some classes of \(\Gamma\)-(semi)hypergroups that we call them weak Sperner \(\Gamma\)-(semi)hypergroups and Sperner \(\Gamma\)-(semi)hypergroups. Then we introduce the class of complete \(\Gamma\)-(semi)hypergroups as a generalization of the class of complete semihypergroups and we show that every complete \(\Gamma\)-(semi)hypergroups is a Sperner \(\Gamma\)-(semi)hypergroups. Finally the class of complementable \(\Gamma\)-(semi)hypergroups is investigated.
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