Generalized Fuzzy Hypergraphs and Hypergroupoids

Abstract

This article presents a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. Firstly, we introduce the notion of generalized fuzzy hypergraph and then, we construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Secondly, we construct higher order fuzzy hypergroupoids and we study their properties. Finally, by considering a regular equivalence relation on a (g-f)$^p$-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.