Hypergroups associated with HX-groups

We have already studied a correspondence between HX-groups and hypergroups. Now we extend this correspondence to semigroups of sub- sets of a group G (and to begin, we considered ℤ₂ × ℤ₃ as group G). Moreover these subsets can have non empty intersection, they can be contained, one in another one. One calculates the fuzzy grade and we find always ∂H = 1.