MULTIVALUED FUNCTIONS, FUZZY SUBSETS AND JOIN SPACES

Abstract

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⎬