Some properties of generalized rough sets

Some algebraic and topological properties of generalized rough sets, associated with generalized lower and upper approximations are studied. Generalized definable sets give rise to two topological spaces. Degree of accuracy (DAG) for generalized rough sets induces two types of equivalence relations, one is defined on X, whereas the other is defined on P(Y). Both of these relations strictly manage an order in classes of X and P(Y). It has been shown that DAG induces two types of fuzzy subsets: one of the set X and the other of P(Y). Finally, some properties of these fuzzy sets have been discussed.