Partitioning Fuzzy C-Means Clustering Algorithms for Interval-Valued Data Based on City-Block Distances

This paper presents partitioning fuzzy c-means clustering algorithms for interval-valued data based on city-block distances. These fuzzy c-means 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 city-block distances between vectors of intervals. The adaptive city-block 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.