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On characterization of \((\mathcal {I},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators

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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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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (Nos. 61473181 and 11771263) and the Fundamental Research Funds for the Central Universities (Nos. GK201702008 and 2016TS034).

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  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China

    Yan-Ling Bao, Hai-Long Yang & Sheng-Gang Li

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  1. Yan-Ling Bao
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Bao, YL., Yang, HL. & Li, SG. On characterization of \((\mathcal {I},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators. Soft Comput 23, 6065–6084 (2019). https://doi.org/10.1007/s00500-018-3613-z

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