Fuzzy clustering algorithm with H-operator applied to problems with interval-based data

The main advantage of using an interval-based distance for interval-based data lies on the fact that it preserves the underlying imprecision on intervals which is usually lost when real-valued distances are applied. One of the main problems when using interval-based distance in fuzzy clustering algorithms is the way to obtain the center of the groups. In this case, it is necessary to make adaptations in order to obtain those centers. Therefore, in this paper, we propose the use of the family of H-operator to proposed three approaches to transform the interval-based membership matrix into real-valued membership matrix and, as a consequence, to calculate the centers of the groups in interval-based fuzzy clustering algorithms. In this case, we will perform a comparative analysis using the three different approaches proposed in this paper, using seven interval-based datasets (four synthetic and three real datasets). As a result of this analysis, we will observe that the proposed approaches achieved better performance than all analyzed methods for interval-based methods.