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Smarandache initiated neutrosophic sets (NSs) as a tool for handling undetermined information. Wang et al. proposed single valued neutrosophic sets (SVNSs) that is an especial NSs and can be used expediently to deal with real-world problems. In this paper, we propose single valued neutrosophic rough sets by combining single valued neutrosophic sets and rough sets. We study the hybrid model by constructive and axiomatic approaches. Firstly, by using the constructive approach, we propose the lower/upper single valued neutrosophic approximation operatorsand illustrate the connections between special single valued neutrosophic relations (SVNRs) and the lower/upper single valued neutrosophic approximation operators. Then, by using the axiomatic approach, we discuss the operatororiented axiomatic characterizations of single valued neutrosophic rough sets. We obtain that different axiom sets of the lower/upper single valued neutrosophic set-theoretic operators guarantee the existence of different classes of SVNRs which produce the same operators. Finally, we introduce single valued neutrosophic rough sets on two-universes and an algorithm of decision making based on single valued neutrosophic rough sets on two-universes, and use an illustrative example to demonstrate the application of the proposed model.