Empirical Sensitivity Analysis on the Influence of the Shape of Fuzzy Data on the Estimation of Some Statistical Measures

This paper means an introduction to analyze whether the choice of the shape for fuzzy data in their statistical analysis can or cannot affect the conclusions of such an analysis. More concretely, samples of fuzzy data are simulated in accordance with different assumptions (distributions) concerning four relevant points (namely, those determining their core and support), and later, by preserving core and support, the 'arms' are changed by considering trapezoidal, Pi-curves, and some LR fuzzy numbers. For the simulations obtained with each of the considered shapes, several characteristics have been estimated: Aumann-type mean, 1-norm and wabl/ldev/rdev medians and Frechet's variance. A comparative analysis with the bias, mean squared distance and variance of the estimates is finally included.