Affiliations: [a] Department of Mathematics, Faculty of Science, Tanta University, Egypt
| [b] Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
| [c] Department of Mathematics, College of Science and Arts, Methnab, Qassim University, Buridah, Saudi Arabia
Correspondence:
[*]
Corresponding author. Dr. El-Sayed Ahmad Abo-Tabl, E-mail: [email protected].
Abstract: The present work proposes new styles of rough sets by using different neighborhoods which are made from a general binary relation. The proposed approximations represent a generalization to Pawlak’s rough sets and some of its generalizations, where the accuracy of these approximations is enhanced significantly. Comparisons are obtained between the methods proposed and the previous ones. Moreover, we extend the notion of “nano-topology”, which have introduced by Thivagar and Richard [49], to any binary relation. Besides, to demonstrate the importance of the suggested approaches for deciding on an effective tool for diagnosing lung cancer diseases, we include a medical application of lung cancer disease to identify the most risk factors for this disease and help the doctor in decision-making. Finally, two algorithms are given for decision-making problems. These algorithms are tested on hypothetical data for comparison with already existing methods.
Keywords: Neighborhoods, topology, rough sets, generalized nano-topology, attributes reduction and lung cancer disease
