Affiliations: Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, China | Department of Mathematics, Yazd University, Yazd, Iran
Note: [] Corresponding author. Jianming Zhan, Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province 445000, China. Tel.: +86 0718-8437732. E-mail: [email protected]
Abstract: The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion of a rough hemiring and a soft hemiring. We study roughness in soft hemirings with respect to Pawlak approximation spaces. Some new rough soft operations are explored. In particular, lower and upper rough soft hemirings and (k-idealistic, h-idealistic, strong h-idealistic) idealistic soft hemirings are investigated. Finally, an important result on an upper strong h-idealistic rough soft hemiring via Bourne's congruence relations are obtained.
