Partitioning fuzzy clustering algorithms for interval-valued data based on Hausdorff distances

This paper presents partitioning fuzzy clustering algorithms for interval-valued data. These fuzzy clustering algorithms give a fuzzy partition and a prototype for each fuzzy cluster by optimizing an adequacy criterion based on suitable adaptive and non-adaptive Hausdorff distances between vectors of intervals. The adaptive Hausdorff distances change at each algorithm iteration and are different from one fuzzy cluster to another. Experiments with real interval-valued data sets show the usefulness of these fuzzy clustering algorithms.