document: Analysis and efficient implementation of a linguistic fuzzy c-means The paper is concerned with a linguistic fuzzy c-means -LRB- FCM -RRB- algorithm with vectors of fuzzy numbers as inputs . This algorithm is based on the extension principle and the decomposition theorem . It turns out that using the extension principle to extend the capability of the standard membership update equation to deal with a linguistic vector has a huge computational complexity . In order to cope with this problem , an efficient method based on fuzzy arithmetic and optimization has been developed and analyzed . We also carefully examine and prove that the algorithm behaves in a way similar to the FCM in the degenerate linguistic case . Synthetic data sets and the iris data set have been used to illustrate the behavior of this linguistic version of the FCM
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