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Rough Approximations Induced by Orthocomplementations in Formal Contexts

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Rough Sets (IJCRS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9920))

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Abstract

Formal contexts is a common framework for rough set theory and formal concept analysis, and some rough set models in formal contexts have been proposed. In this paper, based on the theory of abstract approximation spaces presented by Cattaneo [1], a Brouwer orthocomplementation on the set of objects of a formal context is presented, as a result, a pair of new lower and upper rough approximation operators is introduced. Comparison between the new approximation operators and the existing approximation operators is made, and two necessary and sufficient conditions about equivalence of the operators are obtained. Relationships and algebraic structures among the definable subsets of these approximation operators are investigated.

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Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (Nos. 11071284, 61075120, 61272021, 61202206) and the Zhejiang Provincial Natural Science Foundation of China (Nos. LY14F030001, LZ12F03002, LY12F02021).

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Authors and Affiliations

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

    Tong-Jun Li, Wei-Zhi Wu & Shen-Ming Gu

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

    Tong-Jun Li, Wei-Zhi Wu & Shen-Ming Gu

Authors
  1. Tong-Jun Li
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  2. Wei-Zhi Wu
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  3. Shen-Ming Gu
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Corresponding author

Correspondence to Tong-Jun Li .

Editor information

Editors and Affiliations

  1. Universidad Católica del Norte, Antofagasta, Chile

    Víctor Flores

  2. University of Campinas, Campinas, SP, Brazil

    Fernando Gomide

  3. University of Warsaw, Warsaw, Poland

    Andrzej Janusz

  4. Universidad del Católica del Norte, Antofagasta, Chile

    Claudio Meneses

  5. Tongji University, Shanghai, China

    Duoqian Miao

  6. University of Applied Sciences, Munich, Germany

    Georg Peters

  7. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  8. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  9. Universidad de Chile, Santiago, Chile

    Richard Weber

  10. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

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Li, TJ., Wu, WZ., Gu, SM. (2016). Rough Approximations Induced by Orthocomplementations in Formal Contexts. In: Flores, V., et al. Rough Sets. IJCRS 2016. Lecture Notes in Computer Science(), vol 9920. Springer, Cham. https://doi.org/10.1007/978-3-319-47160-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-47160-0_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47159-4

  • Online ISBN: 978-3-319-47160-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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