A comparison of two types of rough approximations based on N_j-neighborhoods

Article type: Research Article

Authors: Al-shami, Tareq M.^{a; b; *} | Alshammari, Ibtesam^c | El-Shafei, Mohammed E.^a

Affiliations: [a] Department of Mathematics, Mansoura University, Mansoura, Egypt | [b] Department of Mathematics, Sana’a University, Sana’a, Yemen | [c] Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin, Saudi Arabia

Correspondence: [*] Corresponding author. Tareq M. Al-Shami. E-mail: tareqalshami83@gmail.com.

Abstract: In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

Keywords: N_j-neighborhoods, E_j-neighborhoods, j-neighborhood space, lower and upper approximations, accuracy measure, topological space

DOI: 10.3233/JIFS-210272

Journal: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 1, pp. 1393-1406, 2021