The L-fuzzy Nakano hypergroup

In this paper we start with a lattice (X,∨,∧) and define, in terms of ∨, a family of crisp hyperoperations tp (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X,tp) is a join space and the hyperalgebra (X,tp,∧) is very similar to a hyperlattice. Then we use the hyperoperations tp as p-cuts to introduce an L-fuzzy hyperoperation t and show that (X,t) is an L-fuzzy join space and the hyperalgebra (X,tp,∧) is very similar to an L-fuzzy hyperlattice. AMS Classification: 08A72, 03E72, 06B99, 06D30, 20N20.