The aim of this paper is to construct an algebraic hyperstructure over a set G corresponding to a Boolean algebra B and a function S:G B. In order to accomplish this goal we will need to define a hyperoperation on the set G. We define,
a b =
and prove that if the image of G is a ?-semilattice or constitute a partition of 1 in B, then (G, ) is a hypergroup.
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