Clustering Granular Data and Their Characterization With Information Granules of Higher Type

The study is devoted to the clustering of granular data and an evaluation of the results of such clustering. A comprehensive and systematic approach is developed, which is composed of three fundamental phases: 1) representation of granular data; 2) clustering carried out in the representation space of information granules; and 3) evaluation of quality of clusters following the reconstruction criterion. The reconstruction criterion formed originally for numeric data and leading to an idea of granular prototypes is revisited. We show here an emergence of granular information of higher type, which are used to implement granular interval prototypes. We discuss a way of forming granular data in the context of representation of time series and present clustering of granular time series.