CONSTRUCTIVE AND ALGEBRAIC METHODS OF THE THEORY OF ROUGH SETS

This paper reviews and compares constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts f rom a binary relation and defines a pair of lower and upper approximat ion operators using the binary relation. Different classes of rough se t algebras are obtained from different types of binary relations. In t he algebraic approach, one defines a pair of dual approximation operat ors and states axioms that must be satisfied by the operators. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of approximation operators guarantee the existence of c ertain types of binary relations producing the same operators. (C) 199 8 Elsevier Science Inc. All rights reserved.