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International Conference on Rough Sets and Knowledge Technology

RSKT 2015: Rough Sets and Knowledge Technology pp 164–174Cite as

Knowledge Spaces and Reduction of Covering Approximation Spaces

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9436))

Abstract

Theory of covering rough sets is one kind of effective methods for knowledge discovery. In Bonikowski covering approximation spaces, all definable sets on the universe form a knowledge space. This paper focuses on the theoretic study of knowledge spaces of covering approximation spaces. One kind of dependence relations among covering approximation spaces is introduced, the relationship between the dependence relation and lower and upper covering approximation operators are discussed in detail, and knowledge spaces of covering approximation spaces are well characterized by them. By exploring the dependence relation between a covering approximation space and its sub-spaces, the notion of the reduction of covering approximation spaces is induced, and the properties of the reductions are investigated.

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References

  1. Bonikowski, Z., Bryniarski, E., Wybraniec, U.: Extensions and intentions in the rough set theory. Inf. Sci. 107, 149–167 (1998)

    Article  MathSciNet  Google Scholar 

  2. Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Appl. Math. 127, 241–269 (2003)

    Article  MathSciNet  Google Scholar 

  3. Chen, D., Wang, C., Hu, Q.: A new approach to attributes reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf. Sci. 177, 3500–3518 (2007)

    Article  MathSciNet  Google Scholar 

  4. Doignon, J.P., Falmagne, J.C.: Knowledge Spaces. Springer, Heidelberg (1999)

    Book  Google Scholar 

  5. Kortelainen, J.: On the relationship between modified sets, topological spaces and rough sets. Fuzzy Sets Syst. 61, 91–95 (1994)

    Article  MathSciNet  Google Scholar 

  6. Liu, C., Miao, D.Q., Qian, J.: On multi-granulation covering rough sets. Int. J. Approx. Reason. 44, 1404–1418 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Li, T.J., Leung, Y., Zhang, W.X.: Generalized fuzzy rough approximation operators based on fuzzy coverings. Int. J. Approx. Reason. 48, 836–856 (2008)

    Article  MathSciNet  Google Scholar 

  8. Restrepo, M., Cornelis, C., Gomez, J.: Partial order relation for approximation operators in covering based rough sets. Inf. Sci. 284, 44–59 (2014)

    Article  MathSciNet  Google Scholar 

  9. Monjardet, B.: The presence of lattice theory in discrete problems of mathematical social sciences. Why. Math. Soc. Sci. 46, 103–144 (2003)

    Article  MathSciNet  Google Scholar 

  10. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)

    Article  Google Scholar 

  11. Qian, Y.H., Liang, J.Y., Pedrycz, W., Dang, C.Y.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artif. Intell. 174, 597–618 (2010)

    Article  MathSciNet  Google Scholar 

  12. Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowl. Data Eng. 12, 331–336 (2000)

    Article  Google Scholar 

  13. Wang, L., Yang, X., Yang, J.: Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system. Inf. Sci. 207, 66–78 (2012)

    Article  MathSciNet  Google Scholar 

  14. Xu, W.H., Zhang, W.X.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443–2455 (2007)

    Article  MathSciNet  Google Scholar 

  15. Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335–345 (2010)

    Article  MathSciNet  Google Scholar 

  16. Yao, Y.Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16, 87–104 (2001)

    Article  Google Scholar 

  17. Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181, 1080–1096 (2011)

    Article  MathSciNet  Google Scholar 

  18. Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)

    Article  MathSciNet  Google Scholar 

  19. Yue, X.D., Miao, D.Q., Zhang, N., Cao, L.B., Wu, Q.: Multiscale roughness measure for color image segmentation. Inf. Sci. 216, 93–112 (2012)

    Article  Google Scholar 

  20. Zakowski, W.: Approximations in the space \((u,\prod )\). Demonstratio Mathematica 16, 761–769 (1983)

    Article  MathSciNet  Google Scholar 

  21. Zhang, J.B., Li, T.R., Chen, H.M.: Composite rough sets for dynamic data mining. Inf. Sci. 257, 81–100 (2014)

    Article  MathSciNet  Google Scholar 

  22. Zhu, W., Wang, F.-Y.: Covering based granular computing for conflict analysis. In: Mehrotra, S., Zeng, D.D., Chen, H., Thuraisingham, B., Wang, F.-Y. (eds.) ISI 2006. LNCS, vol. 3975, pp. 566–571. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  23. Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)

    Article  MathSciNet  Google Scholar 

  24. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)

    Article  MathSciNet  Google Scholar 

  25. Zhu, W., Wang, F.Y.: The fourth type of covering-based rough sets. Inf. Sci. 201, 80–92 (2012)

    Article  MathSciNet  Google Scholar 

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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, Shen-Ming Gu & Wei-Zhi Wu

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

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

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

Correspondence to Tong-Jun Li .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

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

    Guoyin Wang

  3. Indian Statistical Institute, Kolkata, India

    Sushmita Mitra

  4. Zhejiang Ocean University, Zhejiang, China

    Wei-Zhi Wu

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Li, TJ., Gu, SM., Wu, WZ. (2015). Knowledge Spaces and Reduction of Covering Approximation Spaces. In: Ciucci, D., Wang, G., Mitra, S., Wu, WZ. (eds) Rough Sets and Knowledge Technology. RSKT 2015. Lecture Notes in Computer Science(), vol 9436. Springer, Cham. https://doi.org/10.1007/978-3-319-25754-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-25754-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25753-2

  • Online ISBN: 978-3-319-25754-9

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