A Measurement-Theoretic Axiomatization of Trapezoidal Membership Functions

In many applications of fuzzy set theory, the membership of an object is not defined directly. One of its attributes (like height, age, weight, etc.) is first mapped to a real number (often by means of a physical instrument) and a parametric function then maps this real number to a membership degree in some fuzzy set (like "tall," "old," "heavy," etc.). A very common parametric function is the trapezoidal one. This paper presents some conditions guaranteeing the existence of such a trapezoidal membership function representing the knowledge of an expert. Further experimental research is needed for testing whether these conditions are satisfied by human agents