Toward fuzzy-valued matching and similarity assessment

A fuzzy-valued measure of the degree of matching of two fuzzy sets is proposed based on the Jaccard index applied to the level sets. This measure satisfies a generalization the criteria of Dubois and Prade (1982) for point-valued matching indices. A similarity index is obtained by combining the matching index with a proximity assessment. These fuzzy-valued indices provide a more comprehensive summarization of the similarity of fuzzy sets than the standard point-valued measures.