Connections between fuzzy multi-groups and fuzzy multi-graphs

Abstract

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 $Gamma_wedge^sigma$.