The Paradigm of Granular Rough Computing: Foundations and Applications

Granular Rough Computing is a paradigm within Rough Computing which in turn can be set within the realm of Cognitive Informatics, i.e. machine intelligence tools which emulate cognitive processes in living organisms; its aim is to compute with granules of knowledge that are collective objects formed from individual objects by means of a similarity measure. In this work, we apply the formalism for granule formation proposed by us and studied over last few years which is based on similarity measures called Rough Inclusions. A proper study of rough inclusions has been done within Rough Mereology, a paradigm for approximate reasoning that is rooted in the theory of concepts called Mereology based on the notion of a part instead on the notion of an element like the naive concept theory. We give an outline of granulation theory based on rough inclusions; then, we discuss the most important consequence of similarity among objects in a granule, viz., the hypothesis that granules represent new objects, which preserve the most important features of objects in a granule. This leads to the notion of a granular decision system obtained by means of granulation from an original decision system. The hypothesis that granular decision systems reflect properties of original decision systems to a satisfactory degree, put forth by the author at 2005 and 2006 IEEE GrC conferences, has been tested with very good results. We include here some results of those tests.