Characterization of fuzzy clustering algorithms in terms of entropy of probabilistic sets

We discuss a method of evaluating fuzzy clustering algorithms. Each of them generates a partition matrix of a data set with the entries lying in the [0, 1] interval and expressing the grade of belonging of the object to the clusters detected. Membership functions of the same cluster are interpreted as probabilistic sets in the sense of Hirota. This makes it possible to characterize the clusters by means of the entropy of the corresponding probabilistic sets. Moreover, the mutual entropy of pairs of probabilistic sets provides an index for evaluating the degree of interaction between clusters.