Empirical analysis of the maximum asymptotic bias of location estimators for fuzzy number-valued data

Abstract

Several robust measures to summarize the central tendency of a random fuzzy number have been recently proposed and compared empirically to analyze differences in finite sample behaviour. Although there is no uniformly most appropriate location estimator as in the classical settings, it seems that the empirical results are more influenced by the distributions considered for the generation of the sample data than by other aspects such as the sample size. The aim of this work is to go more deeply into the empirical comparison by investigating the maximum asymptotic bias of the location estimators, which is considered to be the most accurate measure of robustness for point estimators.

Shannon entropy-based approach for calculating values of WABL parameters

“…Sinova and Aelst [21] conducted a simulation study to compare performances of various location estimators such as fuzzy trimmed means, fuzzy Mestimators, sample wabl-median which was suggested based on WABL method, etc. Sinova and Van Aelst [22] designed an empirical study to figure out the maximum asymptotic bias of the fuzzy number-valued measures of central tendency that are Aumann-type sample mean, fuzzy trimmed sample mean, fuzzy M-estimator of location for sample data, 1-norm sample median and wabl/ldev/rdev-median for sample data. They created both contaminated and non-contaminated trapezoidal fuzzy random numbers to compare performances of mentioned location measures.…”