Publication Date



Technical Report: UTEP-CS-23-31

To appear in Proceedings of the 20th World Congress of the International Fuzzy Systems Association IFSA'2023, Daegu, South Korea, August 20-24, 2023.


In contrast to crisp clustering techniques that assign each object to a class, fuzzy clustering algorithms assign, to each object and to each class, a degree to which this object belongs to this class. In the most widely used fuzzy clustering algorithm -- fuzzy c-means -- for each object, degrees corresponding to different classes add up to 1. From this viewpoint, these degrees act as probabilities. There exist alternative fuzzy-based clustering techniques in which, in line with the general idea of the fuzzy set, the largest of the degrees is equal to 1. In some practical situations, the probability-type fuzzy clustering works better; in other situations, the more fuzzy-type technique leads to a more adequate clustering. It is therefore desirable to combine the two techniques, so that one of them will cover the situations where the other method does not work so well. Such combination methods have indeed been proposed. An empirical comparison has shown that out of all these combined methods, the most effective one is the method in which we the use the product of probability and fuzzy degree. In this paper, we provide a theoretical explanation for this empirical result.