This article first generalizes the ordinary fuzzy hypergraphs to generalized fuzzy hypergraphs and it makes a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. We construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Moreover, we construct higher order fuzzy hypergroupoids and study their properties. Finally, by considering a regular equivalence relation on a (g-f)$^p$p-hypergroupoid, we define a quotient (g-f)$^p$-hypergroupoid and we investigate some relationships between diagonal product of hypergroupoids and $p$-product of (g-f)-hypergraphs.