Rough Set Algebras as Description Domains

Article type: Research Article

Authors: Cīrulis, Jānis

Affiliations: Department of Computing, University of Latvia, 19 Raina b., Riga LV-1586, Latvia. [email protected]

Note: [] Address for correspondence: Department of Computing, University of Latvia, 19 Raina b., Riga LV-1586, Latvia

Abstract: Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓ is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.

Keywords: description domain, double Stone algebra, inversion, knowledge ordering, rough set, semi-Boolean domain

DOI: 10.3233/FI-2009-0003

Journal: Fundamenta Informaticae, vol. 90, no. 1-2, pp. 27-41, 2009