Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

Article type: Research Article

Authors: Atef, Mohammed^a | Khalil, Ahmed Mostafa^{b; c} | Li, Sheng-Gang^b | Azzam, A.A.^{d; e; *} | El Atik, Abd El Fattah^f

Affiliations: [a] Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, Egypt | [b] College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China | [c] Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt | [d] Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia | [e] Department of Mathematics, Faculty of Science, New Valley University, Elkharga, Egypt | [f] Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Correspondence: [*] Corresponding author. Abdelfatah Azzam, Tel.: +9665 56345254; E-mail: [email protected] (A. A. Azzam).

Abstract: In this paper, we generalize three types of rough set models based on j-neighborhood space (i.e, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (i.e, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.

Keywords: Rough sets, lower and upper approximations, j-neighborhood, j-adhesion neighborhood, accuracy measure

DOI: 10.3233/JIFS-200482

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 4515-4531, 2020