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Two kinds of multi-level formal concepts and its application for sets approximations

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Abstract

In this paper, we introduce two pairs of operators in fuzzy formal contexts. Based on the proposed operators, we present two kinds of multi-level formal concepts. We also propose two pairs of rough approximation operators by employing the two kinds of multi-level formal concepts. By the proposed rough set approximation operators, we not only approximate a crisp set, but also approximate a fuzzy set. Finally, we discuss the properties of the proposed approximation operators in details.

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Acknowledgments

The authors are very indebted to the anonymous referees for their critical comments and suggestions for the improvement of this paper. This work was also supported by grants from the National Natural Science Foundation of China (Nos. 60963006, 61173181, 61075120), the Humanities and Social Science funds Project of Ministry of Education of China (Nos. 09YJCZH082,11XJJAZH001), the Zhejiang Provincial Natural Science Foundation of China (No. LZ12F03002), and the Science and Technology Project of Qingdao (No. 12-1-4-4-(9)-jch).

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Authors and Affiliations

  1. Computer Engineering Institute, Qingdao Technological University, Qingdao, 266520, Shandong, China

    Mingwen Shao

  2. College of Information Science and Technology, Shihezi University, Shihezi, 832000, Xinjiang, China

    Mingwen Shao

  3. Department of Mathematics, Xinxiang College, Xinxiang, 453000, Henan, China

    Hongzhi Yang

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  1. Mingwen Shao
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  2. Hongzhi Yang
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Correspondence to Mingwen Shao.

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Shao, M., Yang, H. Two kinds of multi-level formal concepts and its application for sets approximations. Int. J. Mach. Learn. & Cyber. 4, 621–630 (2013). https://doi.org/10.1007/s13042-012-0128-2

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  • DOI: https://doi.org/10.1007/s13042-012-0128-2

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