Why Triangular Membership Functions Are Often Efficient in F-Transform Applications: Relation to Interval Uncertainty\\ and Haar Wavelets

Authors

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

Publication Date

12-2017

Comments

Technical Report: UTEP-CS-17-93

Abstract

Fuzzy techniques describe expert opinions. At first glance, we would therefore expect that the more accurately the corresponding membership functions describe the expert's opinions, the better the corresponding results. In practice, however, contrary to these expectations, the simplest -- and not very accurate -- triangular membership functions often work the best. In this paper, on the example of the use of membership functions in F-transform techniques, we provide a possible theoretical explanation for this surprising empirical phenomenon.