Location-free robust scale estimates for fuzzy data

Abstract

In analyzing fuzzy-valued imprecise data statistically, scale measures/estimates play an important role. Scale measures/estimates of datasets are often considered, among others, to descriptively summarize them, to compare the dispersion or the spread of different datasets, to standardize data, to state rules for detecting outliers, to formulate regression objective functions, and so on. To be robust, an estimate of scale should have a finite breakdown point close to 50% (i.e., around half data should be replaced by ‘outliers’ to make the estimate break down, either in the sense of exploding to infinity or imploding to zero). In this respect, the Median Distance Deviation about the median (MDD) for fuzzy datasets has already been introduced and its robust behaviour has been proved. In contrast to the real-valued case, computation of the MDD for fuzzy data is much more complex and cannot be exactly but approximately performed in general.