Why triangular membership functions are often efficient in f-transform applications: Relation to probabilistic and interval uncertainty and to haar wavelets

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.