Algebraic Properties of Generalized Rough Sets
In this paper we consider the problem whether for a map phi : A (B) -> B there is a relation R on A (B) such that properties of a map phi* : B -> B are reflected to R. This is a converse problem that J. Jarvinen proved in [5]. We give an affirmative answer to the problem. Moreover we give equational bases which characterize properties of the map phi. This means that the classes of some types of algebras form varieties. Hence, there are full correspondence between properties of relations and varieties of modal algebras.
generalized rough sets modal algebra atomic boolean algebra