Abstract
Axiomatic characterization is the foundation of rough set theory: the axiom sets of approximation operators guarantee the existence of binary relations, coverings or (generalized) neighborhood systems that reproduce the approximation operators. Focusing on two pairs of generalized neighborhood system-based approximation operators (one pair is defined by Syau and Lin, the other pair is newly defined), we establish their axiomatic characterizations.
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Acknowledgements
The authors thank the reviewers and the area editor for their valuable comments and suggestions. This study was funded by National Natural Science Foundation of China (11501278) and Shandong Provincial Natural Science Foundation, China (ZR2013AQ011, ZR2014AQ011) and the Ke Yan Foundation of Liaocheng University (318011505).
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FZ: The first pair of approximation operators. LL: The second pair of approximation operators.
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Communicated by A. Di Nola.
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Zhao, F., Li, L. Axiomatization on generalized neighborhood system-based rough sets. Soft Comput 22, 6099–6110 (2018). https://doi.org/10.1007/s00500-017-2957-0
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DOI: https://doi.org/10.1007/s00500-017-2957-0