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Abstract
In this paper we show a construction of a hypergoupoid (H, *) from an ordered groupoid (H, •, ≤). Conditions are found for (H, *) to be a semi-hypergroup or hypergroup. As an example we create “hyperarithmetic” of Boolean matrices from an ordered semigroup of Boolean matrices with the operation of a set union. Further we study homomorphisms, good homomorphisms and 2-, 3-, 4-homomorphisms of hyperstructures in question.