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.
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Zhan et al. (2015) studied this question.