Graphs are very powerful representational tools which are very well suited for many computer applications. In handwriting analysis task, graphs often have to be compared to verify the similarity between two handwriting models. Since there is always doubt while models are constructed, the nodes and the edges require fuzzy attributes to properly describe the handwriting character. Adding fuzzy logic to the existing attributed relational graph approach enables us to interpret graph matching result as the similarity to the reference graph. In this article we present a novel approach using a combination of fuzzy logic and attributed relational graph, which named the fuzzy attributed relational graph. Experiments are performed on two databases. The comparison of the proposed approach with the state of the art methods of graph matching highlights its relevance.