Accuracy based on simply* alpha open set in rough set and topological space

M A El Safty; M El Sayed; S A Alblowi

doi:10.1007/s00500-021-05935-7

Accuracy based on simply* alpha open set in rough set and topological space

Soft comput. 2021;25(16):10609-10615. doi: 10.1007/s00500-021-05935-7. Epub 2021 Jul 12.

Authors

M A El Safty¹, M El Sayed², S A Alblowi³

Affiliations

¹ Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif, 21944 Saudi Arabia.
² Department of Mathematics, College of Science and Arts, Najran University, Najran, 66445 Saudi Arabia.
³ Department of Mathematics, College of Science, University of Jeddah, Jeddah, Saudi Arabia.

Abstract

Real-world applications now deal with enormous amounts of data, especially in the area of high dimensional features. In the present study, we provide an approach for the rough set which is simply* alpha open set (briefly, $\overset{M *}{S} - α$ open set). This approach was used to introduce a new concept of separation axioms, from which fundamental properties and theorems of preservation were studied. The relationship between basic properties and preservation theorems was also discussed. New near continuous function definitions have also been developed and their characteristics have been discussed. Through an application presented in the work, the relationship between the simply* alpha open set and near continuous function was justified. The simply* alpha open set was studied by the rough set and accordingly new accuracies were obtained. Moreover, an accurate proposal was examined, which competes with that of the methods of Yao and Pawlak. To obtain the results, MATLAB software has been used.

Keywords: Accuracy; Rough set; Similarity; Simply* alpha open set; Topology concepts.