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S. de la Rosa de Saa, P. Filzmoser, M. Gil, M. Asunción Lubiano:
"On the Robustness of Absolute Deviations with Fuzzy Data";
in: "Strengthening Links Between Data Analysis and Soft Computing", Springer Verlag, 2015, ISBN: 978-3-319-10764-6, 133 - 141.

Often atypical observations separated from the majority or deviate from the general pattern appear in the datasets. Classical estimators such as the sample mean or the sample variance, can be substantially affected by these observations, which are referred to as outliers. Robust statistics provides methods which are not unduly influenced by atypical data.

In this paper an introductory empirical study is developed to compare the robustness of the scale estimator `Median Absolute Deviation´ in contrast to the classical scale estimator `Average Absolute Deviation´ in a fuzzy setting. Both estimators are defined on the basis of the Aumann-type mean, the 1-norm median for random fuzzy numbers along with an L 1-type metric between fuzzy numbers, and some of their properties are examined. Outliers will be introduced in simulated fuzzy data to analyze how much these two estimators are influenced by them.

fuzzy data robustness median absolute deviation average absolute deviation

http://dx.doi.org/10.1007/978-3-319-10765-3_16

http://link.springer.com/chapter/10.1007%2F978-3-319-10765-3_16