Soft set theory was first proposed by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainties. In this paper, we introduce the notion of soft Z-congruence relations and investigate several related properties. Furthermore, we obtain a one-to-one correspondence between soft Z-congruence relations and strong h-idealistic soft hemirings and a one-to-one correspondence between soft Z-congruence relations and soft strong h-ideals. Moreover, we show that the relationships between fuzzy congruence relations and soft congruence relations. Finally, we show that soft homomorphisms of soft hemirings and establish homomorphism theorems for soft hemirings by using soft Z-congruence relations.
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