Discrete and Smoothed Resampling Methods for Interval-Valued Fuzzy Numbers

Abstract

In this article, we propose two new resampling algorithms for the simulation of bootstrap-like samples of interval-valued fuzzy numbers (IVFNs). These methods (namely, the $d$ -method and the $s$ -method) reuse a primary sample (an initial set) of IVFNs to generate a secondary sample, which also consists of this type of fuzzy numbers, and simultaneously utilize existing dependencies in pairs of some characteristic points of IVFNs. During a corresponding resampling step, a nonparametric approach is used. Additionally, we apply a widely used assumption about the Gaussian kernel densities. The proposed methods in some way resemble Efron's bootstrap, but, contrary to this classical approach, they generate “not exactly the same as previous” IVFNs, so it leads to a greater diversity of the obtained secondary sample. We also numerically check the quality of the introduced methods using a few more statistically oriented approaches together with four similarity measures and three types of IVFNs.