Monadic Algebras: a Standpoint on Rough Sets

Abstract

The paper studies complete and incomplete information systems, i.e. basic structures of rough set theory (RST), from the standpoint of monadic Boolean algebras (MBAs). In the first part we recall a simple characterisation of RST as a theory of MBAs. In the second part the paper discusses approximation operators obtained from incomplete information systems. In this case we lose a direct link to MBAs and thus our aim is to obtain an MBA which will additionally be interesting from the perspective of RST. In the third part we consider a simple application of approximation operators based on this MBA.