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　operators　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　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.