Comparison between different kinds of approximations by using a family of binary relations

In this paper, we discuss three types of lower and upper approximations of any set with respect to any relation based on right neighborhood. We generalize these three types of approximations into two ways by using a finite number of any binary relations. The first way based on the intersection of the right neighborhoods for a family of binary relations, the second based on the union and intersection of lower and upper approximations of a set according to a family of binary relations \{R(i) : i = 1,2..... n\}. Also, we make a comparison between these types in tables. (C) 2008 Elsevier B.V. All rights reserved.