The credibilistic fuzzy c means clustering algorithm

Since the introduction of fuzzy clustering by Ruspini (1970), fuzzy logic has provided a family of interesting clustering algorithms which expanded the abilities of `crisp´ techniques. The most popular among these algorithms is the fuzzy c means algorithm (FCM). However, FCM and most of its variants are sensitive to the presence of outliers in the data set. Past attempts to reduce this sensitivity included the addition of a “noise cluster” and the introduction of measures that assess the typicality of a vector to a cluster. In this study we provide additional means for outlier rejection through the introduction of a new variable, the credibility of a vector. Credibility measures the typicality of the vector to the entire data set (not to specific subsets as some previous techniques have done). An outlier is expected to have a low value of credibility compared to a non-outlier. The use of the new variable leads to the credibilistic fuzzy c means algorithm