On Foundations and Applications of the Paradigm of Granular Rough Computing

Granular computing, initiated by Lotfi A. Zadeh, has acquired wide popularity as a tool for approximate reasoning, fusion of knowledge, cognitive computing. The need for formal methods of granulation, and means for computing with granules, has been addressed in this work by applying methods of rough mereology. Rough mereology is an extension of mereology taking as the primitive notion the notion of a part to a degree. Granules are formed as classes of objects which are a part to a given degree of a given object. In addition to an exposition of this mechanism of granulation, we point also to some applications like granular logics for approximate reasoning and classifiers built from granulated data sets. notIons centrAl to grAnulAtIon oF knoWledge Granulation of knowledge is one of important aspects of the way in which the human brain works (see, e.g., Pal, 2004). A vast literature on emulating such aspects of the brain workings as granulation, fusion of knowledge, classification by means of neural networks, fuzzy logics, and so on, does witness the role the computer science society attaches to them. These aspects are studied with at least a twofold purpose. First, to get an insight into the processes of perception, concept formation, and reasoning in the brain; second, to transfer this knowledge into the realm of applications.