The fuzzy median and the fuzzy MAD

An extension of two key robust statistics to fuzzy sets is presented and applied to the fuzzy c-means clustering algorithm. Examples of a robust statistic are the median and the median absolute deviation from the median or MAD, a robust estimate of dispersion. These extensions are derived, and the fuzzy median is applied to the fuzzy c-means clustering algorithm. The modified clustering algorithm shows improved performance in clustering data sets generated by heavy-tailed distributions like the Cauchy distribution.