Methods for the construction of membership functions

In almost every work on fuzzy sets, the existence of membership functions t aking part in the considered model is assumed and it is not studied in dept h whether or not such functions exist. On the other hand, generally the rel ationship between a certain studied characteristic and its referential set is not problematic since it is usually a matter of direct measurement. Howe ver, in a great variety of situations it is necessary to work with properti es whose measurement is not obvious, but is an object of study in itself. I n 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 member ship function cannot be assured. However, the conditions of existence and m ethods for the construction of those membership functions may be based on t he psychological measurement theory. (C) 1999 John Wiley Be Sons, Inc.