Connections between fuzzy multi-groups and fuzzy multi-graphs

Document Type : Original Article


1 Department of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

2 Department Mathematics, Payame Noor University, Tehran, Iran.

3 Department of Mathematics, Payame Noor University, Tehran, Iran


 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 $Aut(\Gamma_\wedge^\sigma)$, where $Aut(\Gamma_\wedge^\sigma)$ is a group of automorphisms of the fuzzy multi-graph $\Gamma_\wedge^\sigma$.