Generalized soft rough sets and generated soft ideal rough topological spaces

Article type: Research Article

Authors: Abd El-Latif, A.M.^{a; b; *}

Affiliations: [a] Department of Mathematics, Faculty of Arts and Science, Northern Border University, Rafha, K.S.A. | [b] Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Correspondence: [*] Corresponding author. A.M. Abd El-Latif, Department of Mathematics, Faculty of Arts and Science, Northern Border University, Rafha, K.S.A.; Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, 11341 Cairo, Egypt. Tel.: +966562692469; +20 1001903231; E-mails: alaa.ali@nbu.edu.sa; alaa_8560@yahoo.com.

Abstract: Soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. The main purpose of soft rough set is reducing the soft boundary region by increasing the lower approximation and decreasing the upper approximation. This paper is devoted to the further generalization of the soft rough set theory by using the ideal notion to reduce the soft boundary region. A new soft rough set model, called soft ideal approximation space, is proposed and its properties are derived. The new soft ideal lower and upper approximation operators are presented and their related properties are surveyed.

Keywords: Rough sets, soft rough set, Pawlak approximation space, soft ideal rough topology

DOI: 10.3233/JIFS-17610

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 517-524, 2018