APROKSIMASI PADA GRUP

(Approximation in a Group)

Abstract

A non-empty set  with binary operations on a set  is called a group if the set satisfies the associative property, the existence of an identity, and the existence of an inverse for each element of the set . A normal subgroup  in group can partition group  into equivalence classes so that a lower approximation and an upper approximation can be formed from the non-empty set  corresponding to the normal subgroup . Let  be a non-empty subset of , the lower approximation of corresponding to the normal subgroup  is defined as the set of elements in where the equivalence class of the element is a subset of  while the upper approximation of  corresponding to the normal subgroup  is defined as the set of elements in where the equivalence class of the element intersects the set . In this paper, we will give more general properties regarding the relationship between the upper approximation and the lower approximation by involving two different normal subgroups of group and two different sets that are subsets of group . Furthermore, we will show the corollary of these properties if we use one normal subgroup and one subset of group .

Keywords: equivalence classes, lower approximation, upper approximation