Towards Granular Computing: Classifiers Induced From Granular Structures

Granular computing as a paradigm is an area frequently studied within the Approximate Reasoning paradigm. Proposed by L. A.Zadeh granular computing has been studied within fuzzy as well as rough set approaches to uncertainty. It is manifest that both theories are immanently related to granulation as fuzzy set theory begins with fuzzy membership functions whose inverse images are prototype granules whereas rough set theory starts with indiscernibility relations whose classes are prototype, or, elementary granules. Many authors have devoted their works to analysis of granulation of knowledge, definitions of granules, methods for combining (fusing) granules into larger objects, applications of granular structures, see, quoted in references works by A. Skowron, T.Y. Lin, Y.Y.Yao, L.Polkowski and others. In this work, the emphasis is laid on granular decision (data) systems: they are introduced, methods of their construction with examples are pointed to, and applications are exhibited; those applications are founded on the basic although often implicit principle of data mining, viz., once a plausible for given data similarity measure is found, objects satisfactorily similar should reveal sufficiently close (or, for that matter identical) class values. In this work, this principle is applied to granules, following the idea presented by L.Polkowski at 2005, 2006 IEEE GrC conferences, that granules built on basis of a similarity relation from a given decision system should consists of objects similar to such a degree that averaging them would lead to new objects which together would constitute a new decision system preserving to a high degree knowledge represented by the original decision system. As knowledge in rough set theory is meant as the classification ability, it seems reasonable to test knowledge content with classifiers as classifier accuracy. This informal idea is tested in this work with some specific tools for granule construction, granular system building, and some well–tested classifiers known in literature for a few data sets from the UCI repository. In the following sections we outline: basic ideas of rough computing, granulation of knowledge, the idea of a granular decision system and we include the results of exemplary tests with real data.