On Fuzzy Corsini's Hyperoperations

Hyperstructures and binary relations have been studied by many researchers, for instance, Chvalina 1, 2 , Corsini and Leoreanu 3 , Feng 4 , Hort 5 , Rosenberg 6 , Spartalis 7 , and so on. A partial hypergroupoid 〈H, ∗〉 is a nonempty setH with a function fromH×H to the set of subsets of H. A hypergroupoid is a nonempty set H, endowed with a hyperoperation, that is, a function fromH ×H to P H , the set of nonempty subsets ofH. IfA,B ∈ P H − {∅}, then we defineA ∗B ∪{a ∗ b | a ∈ A, b ∈ B}, x ∗B {x} ∗B and A ∗ y A ∗ {y}. A Corsini’s hyperoperation was first introduced by Corsini 8 and studied by many researchers; for example, see 3, 8–15 .