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Fuzzy rough set models over two universes

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Abstract

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present new extensions of the rough set model over two different universes which are rough fuzzy set model in a generalized approximation space, rough set model in a fuzzy approximation space and rough fuzzy set model in a fuzzy approximation space based over two different universes. Moreover, the properties of the approximation operators in these models are investigated. Furthermore, by employing cut set of fuzzy set and fuzzy relation, classical representations of fuzzy rough approximation operators are studied. Finally, the measures of fuzzy rough set models are presented, and the relationships among the fuzzy rough models and rough set model over two universes are investigated.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (No.61105041,71071124,11071284 and 11001227), National Natural Science Foundation of CQ CSTC (No. cstc2011jjA40037), Science and Technology Program of Board of Education of Chongqing (KJ120805) and Graduate Innovation Foundation of Chongqing University of Technology (No.YCX2011312).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, People’s Republic of China

    Weihua Xu, Wenxin Sun & Yufeng Liu

  2. School of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Wenxiu Zhang

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  1. Weihua Xu
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  2. Wenxin Sun
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Correspondence to Weihua Xu.

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Xu, W., Sun, W., Liu, Y. et al. Fuzzy rough set models over two universes. Int. J. Mach. Learn. & Cyber. 4, 631–645 (2013). https://doi.org/10.1007/s13042-012-0129-1

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  • DOI: https://doi.org/10.1007/s13042-012-0129-1

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