Hypergroups associated with HX-groups

Abstract 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

History and new possible research directions of hyperstructures

We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

HX-groups and Hypergroups

Abstract One considers the hypergroups associated with the HX-groups Z=nZ and with the set of square matrices of order 2, with coefficients in Z=2Z and one calculates their fuzzy grade

MULTIVALUED FUNCTIONS, FUZZY SUBSETS AND JOIN SPACES

One has considered the Hypergroupoid Η Γ = associated with a multivalued function Γ from H to a set D, defined as follows:∀ x ∈ H, x ο Γ x = ⎨y⏐ Γ(y) ∩ Γ(x) ≠ ∅⎬ ,∀ (y,z) ∈ H 2 , y ο Γ z = y ο Γ y ∪ z ο Γ z ,and one has calculated the fuzzy grade ∂(Η Γ ) for several functions Γ defined on sets H, such that ⎮H⎮ ∈ ⎨3, 4, 5, 6, 8, 9, 16⎬