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 sin- gle 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 oper- ators and 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 operator- oriented axiomatic characterizations of single valued neutro- sophic rough sets. We obtain that different axiom sets of the lower/upper single valued neutrosophic set-theoretic oper- ators guarantee the existence of different classes of SVNRs which produce the same operators. Finally, we introduce sin- gle 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 illustra- tive example to demonstrate the application of the proposed model.