Measures of similarity among fuzzy concepts: A comparative analysis

Abstract

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 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.

Fuzzy Repertory Table: A Method for Acquiring Knowledge About Input Variables to Machine Learning Algorithm

“…Since all the values in the fuzzy repertory table are represented as if they were fuzzy values, i.e., by means of a trapezoidal function, we need an analysis technique that uses a measurement for comparing fuzzy sets. Numerous measures of comparison between fuzzy sets can be found in the literature [10], [11], [33]. We shall require from the measure of comparison selected, , the following properties.…”

Fuzzy Sets: History and Basic Notions

“…For surveys, on similarity indices, see Zwick et al (1987) who report on a comparative psychometric experiment indicating that the counting-based indices seem to be less faithful to human perception of similatity that those focusing on some level-cut. Especially, 1 -O(F, G) performs well.…”

“…The major reference on this topic is the book by Diamond and Kloeden (1994) (See also Chapter 11 by Diamond and Kloeden in this volume). Zwick et al (1987) reviews many early proposals of such distances, which they test along with set-theoretic equality indices, for their psychological plausibility. Lowen and Peeters (1998) provide an extensive study of a class of distances between fuzzy sets for which the triangle inequality is not fulfilled.…”

Collaborative Recommendations Using Bayesian Networks and Linguistic Modelling

“…Given two possibility distributions, a one parameter class of distance functions can be defined as [12]:…”