Statistical based fuzzy sets

Abstract

We present a methodology for semantic fuzzy sets. We construct alpha-cuts on the basis of observed data. Therefore we no longer need exclusively triangles, trapeziums or Gauss curves as elementary forms for fuzzy sets. In addition to that, we are able to integrate expert opinions, modelled as fuzzy sets. The methodology combines statistical interval estimation and distribution tests with fuzzy logic. It is applicable to random processes with an insufficient number of sample points. If the sample size increases, the result converges toward the statistical estimators. We applied the method to estimate the discharge of a river.