Some remarks on congruences obtained from the L-fuzzy Nakano hyperoperation

In this paper we study relations which are congruences with respect to ∧ and ⊔p, where ⊔p is the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R1 which is a congruence with respect to ∧ and ⊔1 and, for each p ∈ X, construct an equivalence relation Rp which is a congruence with respect to ∧ and ⊔p. Furthermore, for each x ∈ Rp we construct a quotient hyperoperation ⊔p and we show that the hyperalgebra (X/Rp, ⊔p) is a join space and the hyperalgebra (X/Rp, ⊔p, ∧p) is a hyperlattice.