Why Triangular and Trapezoid Membership Functions: A Simple Explanation

Abstract

In principle, in applications of fuzzy techniques, we can have different complex membership functions. In many practical applications, however, it turns out that to get a good quality result – e.g., a good quality control – it is sufficient to consider simple triangular and trapezoid membership functions. There exist explanations for this empirical phenomenon, but the existing explanations are rather mathematically sophisticated and are, thus, not very intuitively clear. In this paper, we provide a simple – and thus, more intuitive – explanation for the ubiquity of triangular and trapezoid membership functions.