23 research outputs found
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
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
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
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⎬