Methods for the Construction of Membership Functions

In almost every work on fuzzy sets, the existence of membership functions taking part in the considered model is assumed and it is not studied in depth whether or not such functions exist. On the other hand, generally the relationship between a certain studied characteristic and its referential set is not problematic since it is usually a matter of direct measurement. However, in a great variety of situations it is necessary to work with properties whose measurement is not obvious, but is an object of study in itself. In this work, we start by approaching the description of the cases in which the existence of a membership function can be guaranteed. Next, we consider the situations where one faces linguistic terms associated with attributes that cannot be directly measured; in such cases, the existence of a membership function cannot be assured. However, the conditions of existence and methods for the construction of those membership functions may be based on the psychological measurement theory. Q 1999 John Wiley & Sons, Inc.