The properties of a fuzzy-valued index of the degree of matching of two fuzzy sets and its relationship to point-valued measures are examined. The fuzzy matching index is based on the Jaccard index applied to the level sets. Assessing the degree of matching using a fuzzy set produces a more comprehensive summarization of similarity than can be obtained using the standard point-valued indices. The fuzzy-valued index is shown to satisfy a generalization the criteria of Dubois and Prade for matching indices. The fuzzy set representation increases the range of criteria that can be specified and used as thresholds in applications that employ matching in selection or inference.