Measures of similarity among fuzzy concepts: A comparative analysis

Many 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 o f fuzzy concepts as either "'similar" or "'dissimilar, "" all measures performed well. For distinguishing between degrees o f 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" o f the membership function. Such measures are easiest to compute and may provide insight into the way humans judge similarity among fuzzy concepts. K E Y W O R D S : similarity measures, f u z zy concepts *This research was supported by contract MDA 903-83-K-0347 from the U.S. Army Research Institute. The views, opinions, and findings contained in this article are those of the authors and should not be construed as official Department of the Army position, policy, or decision. This work was also supported by a National Science Foundation Grant DMS 840-0602 to Edward Carlstein. Address correspondence to Rami Zwick, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213. International Journal of Approximate Reasoning 1987; 1:221-242 © 1987 Elsevier Science Publishing Co., Inc. 52 Vanderbilt Ave., New York, NY 10017 0888-613X/87/$3.50 221 222 Rami Zwick et al.