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In everyday life, many properties or concepts we encumber are fuzzy in nature. To include those fuzzy properties in solving some types of problems, we have extended the attributed graph to fuzzy-attribute graph (FAG). With such extension, equality of attributes can no longer be used when matching of FAG's is considered, as equality of two fuzzy sets is too strigent a condition. In the paper, fuzzy-attribute graph is formally defines and a new measure for matching two FAG's is suggested. Yhe new measure has its interpretation under fuzzy logic. The model is applied to the recognition of handprinted Chinese characters and the result is presented.