An alternative approach to the fuzzifier in fuzzy clustering to obtain better clustering

The most common fuzzy clustering algorithms are based on the minimization of an objective function that evaluates (fuzzy) cluster partitions. The generalisation step from hard clustering to crisp clustering requires the introduction of an additional parameter, the so called fuzzifier. This fuzzifier does not only control, how much clusters may overlap, but has also some undesired consequences. For example, data have (almost) always non-zero membership degrees to all clusters, no matter how far they are away from a cluster. We propose a concept that generalizes the idea of the fuzzifier and solves the mentioned problems.