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. Further results are included in the paper by Polkowski and Artiemjew [29] in these Proceedings.