Granular description of data: Building information granules with the aid of the principle of justifiable granularity

Formed as generic building blocks being reflective of domain knowledge and experimental numeric evidence, information granules play a pivotal role in processing realized in Granular Computing and facilitating communication with the environment. In this study, we are concerned with a fundamental problem of constructing a collection of meaningful, easily interpretable spherical information granules with the use of the principle of justifiable granularity. The design process is formulated as an optimization problem. First, a series of numeric prototypes are determined around which information granules are constructed. Second, the values of radii of these information granules are optimized aiming at maximizing a certain performance index. Two alternatives of determining centers of information granules are compared, i.e., randomly selected numeric prototypes and prototypes generated with the aid of clustering. Two optimization criteria are also introduced and studied. Experimental studies involving synthetic data as well as data coming from the UCI Machine Learning repository are reported.