Granular Computing and Rough Sets - An Incremental Development

Abstract

SummaryThis chapter gives an overview and refinement of recent works on binary granular computing. For comparison and contrasting, granulation and partition are examined in parallel from the prospect of rough Set theory (RST).The key strength of RST is its capability in representing and processing knowledge in table formats. Even though such capabilities, for general granulation, are not available, this chapter illustrates and refines some such capability for binary granulation. In rough set theory, quotient sets, table representations, and concept hierarchy trees are all set theoretical, while in binary granulation, they are special kind of pretopological spaces, which is equivalent to a binary relation Here a pretopological space means a space that is equipped with a neighborhood system (NS). A NS is similar to the classical NS of a topological space, but without any axioms attached to it3.