Studies in Computational Intelligence 445

Fuzzy clustering comprises a family of prototype-based clustering meth-ods that can be formulated as the problem of minimizing an objective function.These methods can be seen as “fuzzifications” of, for example, the classical c-meansalgorithm, which strives to minimize the sum of the (squared) distances between thedata points and the cluster centers to which they are assigned. However, it is wellknown that in order to “fuzzify” such a crisp clustering approach, it is not enough tomerely allow values from the unit interval for the variables encoding the assignmentsof the data points to the clusters (that is, for the elements of the partition matrix):the minimum is still obtained for a crisp data point assignment. As a consequence,additional means have to be employed in the objective function in order to obtainactual degrees of membership. This paper surveys the most common fuzzificationmeans and examines and compares their properties.