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On the characterization of fuzzy rough sets based on a pair of implications

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Abstract

Ouyang et al. (Inf Sci 180:532–542, 2010) introduced the concept of (I, J)-fuzzy rough sets based on a pair of implications. Considering axiomatic characterization of approximation operators play a significant role in rough set theory, this paper devotes mainly to characterizing (I, J)-fuzzy rough sets based on a pair of implications from both constructive and axiomatic approaches. We firstly investigate the relationship between the lower and upper approximation operators based on a pair of ordinary implications and special fuzzy relations. And then (I, J)-fuzzy rough operators based on some special fuzzy relations are characterized by single axioms, which ensure the existence of polytypic fuzzy relations generating the same (I, J)-fuzzy rough approximation operators.

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Acknowledgements

The authors would like to thank the anonymous referees and the Editor-in-Chief for their valuable comments. This work was funded by the National Natural Science Foundation of China (Grant Nos. 61673352, 41631179, 61573321).

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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, China

    Dechao Li & Weizhi Wu

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, Zhejiang, China

    Dechao Li & Weizhi Wu

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  1. Dechao Li
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  2. Weizhi Wu
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Correspondence to Dechao Li.

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Li, D., Wu, W. On the characterization of fuzzy rough sets based on a pair of implications. Int. J. Mach. Learn. & Cyber. 9, 2081–2092 (2018). https://doi.org/10.1007/s13042-017-0690-8

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  • DOI: https://doi.org/10.1007/s13042-017-0690-8

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