(untitled) (European Journal of Pure and Applied Mathematics, 2017)
The aim is to show that the theory of hypersemigroups and the theory of fuzzy hypersemigroups are parallel to each other, in the following sense: An hypersemigroupH is intra-regular, for example, if and only if ABB*A for every right ideal A and every left ideal B of H. And an hypersemigroupH is intra-regular if and only if fgg° f for every fuzzy right ideal f and every fuzzy left ideal g of H. An hypersemigroupH is left quasi-regular if and only if ABA*B for every ideal A and every nonempty subset B of H. And an hypersemigroupH is left quasi-regular if and only if fgf° g for every fuzzy ideal f and every fuzzy subset g of H.