9.9 rough Set theory 265
The partition induced by B is called a classification of U created by B. The
ordered pair A = (U,B ) is called an approximation space. Conceptually, let R
be a collection of equivalence relations on U; then the pair (U,R) is called
the Pawlak knowledge base.
9.9.2 Rough Sets
The rough set theory (Pawlak, 1991) is not an alternative to classical set
theory, as is fuzzy set theory, but rather is embedded in it. Rough set theo-
ry can be viewed as a specific implementation of Frege’s idea of vagueness.
This means that imprecision in this approach is expressed by a boundary
region of a set and not by a partial membership, as in fuzzy set theory.
The rough set concept can be defined by means of topological opera-
tions, ...