Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation
Przemysław Grzegorzewski, Olgierd Hryniewicz, Maciej Romaniuk
Abstract
Several new resampling methods for generating bootstrap samples of fuzzy numbers are proposed.To avoid undesired repetitions in the secondary samples we do not draw randomly directly observations from the primary samples but construct them allowing for some modifications in their membership functions, however only such which do not disturb the canonical representation of the initial fuzzy numbers.We consider both two-parameter and three-parameter canonical representations, as well as the triangular and trapezoidal outputs in the secondary samples.Numerical experiments concerning some statistical tests based on fuzzy samples show that the suggested methods may appear helpful in statistical reasoning with imprecise data.