The L-fuzzy Nakano hypergroup

In this paper we start with a lattice (X, ∨, ∧) and define, in terms of ∨, a family of crisp hyperoperations ⊔p (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X, ⊔p) is a join space and the hyperalgebra (X, ⊔p, ∧) is very similar to a hyperlattice. Then we use the hyperoperations ⊔p as p-cuts to introduce an L-fuzzy hyperoperation ⊔ and show that (X, ⊔) is an L-fuzzy join space and the hyperalgebra (X, ⊔p, ∧) is very similar to an L-fuzzy hyperlattice.