Neighborhood operator systems and approximations

This paper presents a framework for the study of generalizing the standard notion of equivalence relation in rough set approximation space with various categories of k-step neighborhood systems. Based on a binary relation on a finite universe, six families of binary relations are obtained, and the corresponding six classes of k-step neighborhood systems are derived. Extensions of Pawlak's rough set approximation operators based on such neighborhood systems are proposed. Properties of neighborhood operator systems and rough set approximation operators are investigated, and their connections are examined. (C) 2002 Elsevier Science Inc. All rights reserved.