ROUGH RINGS, ROUGH SUBRINGS, AND ROUGH IDEALS - Agusfrianto, Fakhry Asad; Fitriani, Fitriani; Mahatma, Yudi (Diponegoro University, 2022)
The basic concept in algebra that is set theory can be expanded into rough sets. Basic operations on the set such as intersections, unions, differences, and complements can still apply to rough sets. In addition, one of the applications of rough sets is the use of rough matrices in decision making. Furthermore, mathematical or informatics researchers who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Since the research related to rough sets is mostly carried out at the same time, different concepts have emerged related to rough sets and rough algebraic structures. In this paper, other definitions of rough ring and rough subring will be given along with related examples and theorems. Furthermore, it will also be defined the left ideal and the right ideal of the rough ring along with examples. Finally, we will discuss the theorem regarding rough ideals.