What Is Fuzzy about Fuzzy Clustering? Understanding and Improving the Concept of the Fuzzifier

The step from the well-known c-means clustering algorithm to the fuzzy c-means algorithm and its vast number of sophisticated extensions and generalisations involves an additional clustering parameter, the so called fuzzifier. This fuzzifier controls how much clusters may overlap. It also has some negative effects causing problems for clusters with varying data density, noisy data and large data sets with a higher number of clusters. In this paper we take a closer look at what the underlying general principle of the fuzzifier is. Based on these investigations, we propose an improved more general framework that avoids the undesired effects of the fuzzifier.