Fuzzy S-Estimators

The central tendency and scale of the distribution of a random fuzzy number have been estimated through several measures in the literature. The best-known measures, the Aumann-type mean and the standard deviation, lack robustness and become unreliable under data contamination. With respect to the other approaches, with a more robust behaviour, scale estimators corresponding to the fuzzy medians and fuzzy trimmed means are available, but there is not any natural choice regarding M-estimators of location. In the real-valued setting, S-estimators of location present a similar behaviour to M-estimators and they are associated with a scale estimator. Therefore, the notion of S-estimator will be adapted to the fuzzy-valued case and its practical interest will be illustrated by means of some simulation studies.