Rough Set Algebras as Description Domains
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 down arrow a 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.
rough set description domain knowledge ordering inversion double stone algebra semi-boolean domain