Affiliations: [a] School of Science, Xi’an Technological University, Xi’an, P.R. China
| [b] Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
Correspondence:
[*]
Corresponding author. Ahmed Mostafa Khalil, Department of
Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt.
Tel.: +0201157633794; E-mail: a.khalil@azhar.edu.eg.
Abstract: In this paper, we will propose the novel notion of neighborhood rough sets on a universe set and study some of their basic properties. Then, the relationships between the neighborhood rough sets and covering rough sets are established. Further, the several related notions of probabilistic neighborhood rough sets are investigated and their basic theoretical are discussed. In addition, the notion of neighborhood rough sets over two different universes is defined, and interesting in their properties are explained. Depend on the neighborhood rough sets over two different universes, two algorithms are designed to solve the rough decision-making problems and clarify their applicability by two illustrative examples, respectively. Finally, a comparison between Liu et al.’s approach and our approach is given.
