Fuzzy order statistics and their application to fuzzy clustering

Authors:
P. R. Kersten
Affiliations:
Dept. of Comput. Sci., Midwestern State Univ., Wichita Falls, TX
Venue:
IEEE Transactions on Fuzzy Systems
Year:
1999

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Abstract

The median and the median absolute deviation (MAD) are robust statistics based on order statistics. Order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy MAD. The fuzzy c-means (FCM) clustering algorithm is defined for any p-norm (pFCM), including the l1-norm (1FCM), The 1FCM clustering algorithm is implemented via the alternating optimization (AO) method and the clustering centers are shown to be the fuzzy median. The resulting AO-1FCM clustering algorithm is called the fuzzy c-medians (FCMED) clustering algorithm. An example illustrates the robustness of the FCMED