A kind of new rough set: Rough soft sets and rough soft rings

Article type: Research Article

Authors: Zhan, Jianming^{a; *} | Davvaz, Bijan^b

Affiliations: [a] Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, China | [b] Department of Mathematics, Yazd University, Yazd, Iran

Correspondence: [*] Corresponding author. Jianming Zhan, Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province 445000, China.Tel.: +86 0718-8437732. E-mail: zhanjianming@hotmail.com.

Abstract: The aim of this paper is to lay a foundation for providing a rough soft tool in considering many problems that contain uncertainties. We put forward the concepts of rough soft rings and rough idealistic soft rings. Some basic operations on rough soft rings are discussed. Some good examples are explored. Special attention is paid to rough prime idealistic soft rings. Finally, we investigate some properties of products and sums of rough soft rings.

Keywords: Rough soft set, rough soft ring, congruence, Pawlak approximation space, rough prime idealistic soft ring

DOI: 10.3233/IFS-151772

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 475-483, 2016