On the structure of generalized rough sets

In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1. Any reflexive binary relation determines a topology. 2. If theta is a reflexive and symmetric relation on a set X, then O = {A subset of X\theta_ (A) = A} is a topology such that A is open if and only if it is closed. 3. Conversely, for every topological space (X, O) satisfying the condition that A is open if and only if it is closed, there exists a reflexive and symmetric relation R such that O = {A subset of X\R_ (A) = A}. 4. Let theta be an equivalence relation on X. For any pseudo omega-closed subset A of X, theta_(A) is an omega-closed set if and only if omega(x,x...., x) is an element of theta_(A) for any x is an element of X. Moreover we consider properties of generalized rough sets. (C) 2005 Elsevier Inc. All rights reserved.