Unifying Rough Set Theories via Large Scaled Granular Computing

This paper explains the mathematics of large scaled granular computing (GrC), augmented with a new Knowledge theory, by unifying rough set theories (RS) into one single concept, namely, neighborhood systems (NS). NS was first introduced in 1989 by T. Y. Lin to capture the concepts of “near” (topology) and “conflict” (security). Since 1996 when the term Granular Computing (GrC) was coined by T. Y. Lin to label Zadeh's vision, NS has been pushed into the “heart” of GrC. In 2011, LNS, the largest NS, was axiomatized; it implied that this set of axioms defines a new mathematics that realizes Zadeh's vision. The main messages are: this new mathematics is powerful and practical.