Why Trapezoidal and Triangular Membership Functions Work So Well: Towards a Theoretical Explanation

Authors

Aditi Barua, The University of Texas at El PasoFollow
Lalitha Snigdha Mudunuri, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

8-1-2013

Comments

Technical Report: UTEP-CS-13-50

To appear in Journal of Uncertain Systems, 2014, Vol. 8.

Abstract

In fuzzy logic, an imprecise ("fuzzy") property is described by its membership function μ(x), i.e., by a function which describes, for each real number x, to what degree this real number satisfies the desired property. In principle, membership functions can be of different shape, but in practice, trapezoidal and triangular membership functions are most frequently used. In this paper, we provide an interval-based theoretical explanation for this empirical fact.