Assigning Membership in a Fuzzy Set Analysis

This article provides a largely nontechnical discussion of the acquisition of membership values in fuzzy set analyses. First the basic properties of a membership are discussed. Then the three common strategies of membership assignment—direct subjective assignment, indirect subjective assignment, and transformation—are critically examined in turn. Examples are used to illustrate the techniques. The connection with existing psychometric and statistical methods is particularly emphasized, focusing on the notion of a membership value as a random variable as a means to assess uncertainty in assignment.