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General relation-based variable precision rough fuzzy set

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Abstract

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

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Acknowledgments

The authors are very grateful to the Editor in Chief Professor Xi-Zhao Wang, and the three anonymous referees for their thoughtful comments and valuable suggestions which lead to a significant improvement on the manuscript. E. C. C. Tsang was supported by the Macao Science and Technology Development Fund \(\#002/2011/A\) and Fund \(\#100/2013/A3.\) B. Sun was supported by the National Science Foundation of China (71571090, 71161016), the Fundamental Research Funds for the Central Universities (JB150605), the Chinese Postdoctoral Science Foundation (XJS15067).

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Authors and Affiliations

  1. The Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macau, People’s Republic of China

    Eric C. C. Tsang

  2. School of Economics and Management, Xidian University, Xi’an, 710071, People’s Republic of China

    Bingzhen Sun

  3. School of Economics and Management, Tongji University, Shanghai, 200092, People’s Republic of China

    Weimin Ma

Authors
  1. Eric C. C. Tsang
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  2. Bingzhen Sun
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  3. Weimin Ma
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Correspondence to Bingzhen Sun or Weimin Ma.

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Tsang, E.C.C., Sun, B. & Ma, W. General relation-based variable precision rough fuzzy set. Int. J. Mach. Learn. & Cyber. 8, 891–901 (2017). https://doi.org/10.1007/s13042-015-0465-z

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