Connections between fuzzy multi-groups and fuzzy multi-graphs

In this paper, we introduce the concept of fuzzy multi-graphs and a type of isomorphism on fuzzy multi-graphs and study their properties. We show that how to assign a fuzzy multi-graph to the appropriate fuzzy multi-groups. We also prove that every fuzzy multi-group of group G can be embedded into the fuzzy multi-group of the group Aut(Γσ ), where Aut(Γσ ) is a group of automorphisms of the fuzzy multi-graph Γσ .