Why Empirical Membership Functions Are Well-Approximated by Piecewise Quadratic Functions: Theoretical Explanation for Empirical Formulas of Novak's Fuzzy Natural Logic

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-1-2024

Comments

Technical Report: UTEP-CS-24-32

Abstract

Empirical analysis shows that membership functions describing expert opinions have a shape that is well described by a smooth combination of two quadratic segments. In this paper, we provide a theoretical explanation for this empirical phenomenon.