Monadic Algebras: a Standpoint on Rough Sets

Issue title: Advances in Rough Set Theory

Article type: Research Article

Authors: Wolski, Marcin

Affiliations: Department of Logic and Methodology of Science, Maria Curie-Skłodowska University, Poland. marcin.wolski@umcs.lublin.pl

Note: [] Address for correspondence: Department of Logic and Methodology of Science, Maria Curie-Skłodowska University, Poland

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.

DOI: 10.3233/FI-2011-419

Journal: Fundamenta Informaticae, vol. 108, no. 3-4, pp. 181-196, 2011