Abstract
This paper presents a general framework for the study of $$({\mathcal {I}}, {\mathcal {N}})$$ -single valued neutrosophic rough sets from constructive and axiomatic perspectives. In the constructive approach, a pair of single valued neutrosophic rough approximation operators based on single valued neutrosophic implicator $${\mathcal {I}}$$ and single valued neutrosophic norm $${\mathcal {N}}$$ is first proposed. Moreover, some basic properties of $$({\mathcal {I}},{\mathcal {N}})$$ -single valued neutrosophic rough approximation operators are explored. In addition, connections between single valued neutrosophic relations and $$(\mathcal {I},{\mathcal {N}})$$ -single valued neutrosophic rough approximation operators are systematically discussed. In the axiomatic approach, axiomatic characterization of $$({\mathcal {I}},{\mathcal {N}})$$ -single valued neutrosophic approximation operators is studied. Specifically, different axiom sets characterizing the intrinsic properties of $$(\mathcal {I},{\mathcal {N}})$$ -single valued neutrosophic rough approximation operators associated with diverse single valued neutrosophic relations are investigated in detail.
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