Measures of similarity among fuzzy concepts: A comparative analysis

AbstractMany measures of similarity among fuzzy sets have been proposed in the literature, and some have been incorporated into linguistic approximation procedures. The motivations behind these measures are both geometric and set-theoretic. We briefly review 19 such measures and compare their performance in a behavioral experiment. For crudely categorizing pairs of fuzzy concepts as either “similar” or “dissimilar,” all measures performed well. For distinguishing between degrees of similarity or dissimilarity, certain measures were clearly superior and others were clearly inferior; for a few subjects, however, none of the distance measures adequately modeled their similarity judgments. Measures that account for ordering on the base variable proved to be more highly correlated with subjects' actual similarity judgments. And, surprisingly, the best measures were ones that focus on only one “slice” of the membership function. Such measures are easiest to compute and may provide insight into the way humans judge similarity among fuzzy concepts