Set-Theoretic Models of Granular Structures

  • Yiyu Yao
  • Duoqian Miao
  • Nan Zhang
  • Feifei Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)


Granular structure is one of the fundamental concepts in granular computing. Different granular structures reflect multiple aspects of knowledge and information, and depict the different characteristics of data. This paper investigates a family of set-theoretic models of different granular structures. The proposed models are particularly useful for concept formulation and learning. Some of them can be used in formal concept analysis, rough set analysis and knowledge spaces. This unified study of granular structures provides a common framework integrating these theories of granular computing.


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  1. 1.
    Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)Google Scholar
  2. 2.
    Caspard, N., Monjardet, B.: Some lattices of closure systems on a finite set. Discrete Mathematics and Theoretical Computer Science 6, 163–190 (2004)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Doignon, J.P., Falmagne, J.C.: Knowledge Spaces. Springer, Berlin (1999)zbMATHGoogle Scholar
  4. 4.
    Hobbs, J.R.: Granularity. In: Joshi, A. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 432–453. IEEE Computer Society Press, Los Angeles (1985)Google Scholar
  5. 5.
    Keet, C.M.: A Formal Theory of Granularity, PhD Thesis, KRDB Research Centre, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy (2008), (accessed June 8, 2008)
  6. 6.
    Lin, T.Y., Yao, Y.Y., Zedah, L.A. (eds.): Data Mining, Rough Set and Granular Computing. Physica-Verlag, Heidelberg (2002)Google Scholar
  7. 7.
    Miao, D.Q., Fan, S.D.: The calculation of knowledge granulation and its application. System Engeering-Theory and Practice 1, 48–56 (2002)Google Scholar
  8. 8.
    Miao, D.Q., Wang, G.Y., Liu, Q., Lin, T.Y., Yao, Y.Y. (eds.): Granular Computing: Past, Present and Prospect. Tsinghua University Press, Beijing (2007)Google Scholar
  9. 9.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)zbMATHGoogle Scholar
  11. 11.
    Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley Interscience, New York (2008)Google Scholar
  12. 12.
    Shiu, L.P., Sin, C.Y.: Top-down, middle-out, and bottom-up processes: a cognitive perspective of teaching and learning economics. International Review of Economics Education 5, 60–72 (2006)Google Scholar
  13. 13.
    Wille, R.: Concept lattices and conceptual knowledge systems. Computers Mathematics with Applications 23, 493–515 (1992)zbMATHCrossRefGoogle Scholar
  14. 14.
    Xu, F.F., Yao, Y.Y., Miao, D.Q.: Rough set approximations in formal concept analysis and knowledge spaces. In: An, A., Matwin, S., Raś, Z.W., Ślęzak, D. (eds.) ISMIS 2008. LNCS (LNAI), vol. 4994, pp. 319–328. Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Yao, Y.Y.: On generalizing Pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 298–307. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y.: Perspectives of granular computing. In: Hu, X.H., Liu, Q., Skowron, A., Lin, T.Y., Yager, R.R., Zhang, B. (eds.) Proceedings of 2005 IEEE International Conference on Granular Computing (GrC 2005), pp. 85–90. IEEE Computer Society Press, Los Angles (2005)CrossRefGoogle Scholar
  18. 18.
    Yao, Y.Y.: Three perspectives of granular computing. Journal of Nanchang Institute of Technology 25, 16–21 (2006)Google Scholar
  19. 19.
    Yao, Y.Y.: Granular computing: past, present and future. In: Hu, X.H., Hata, Y., Slowinski, R., Liu, Q. (eds.) Proceedings of 2008 IEEE International Conference on Granular Computing (GrC 2008), pp. 80–85. IEEE Computer Society Press, Los Angles (2008)CrossRefGoogle Scholar
  20. 20.
    Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Transactions on Systems, Man, and Cybernetics (Part B) 4, 855–866 (2009)CrossRefGoogle Scholar
  21. 21.
    Yao, Y.Y., Miao, D.Q., Xu, F.F.: Granular Structures and Approximations in Rough Sets and Knowledge Spaces. In: Ajith, A., Rafael, F., Rafael, B. (eds.) Rough Set Theory: A True Landmark in Data Analysis. Springer, Berlin (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yiyu Yao
    • 1
  • Duoqian Miao
    • 2
  • Nan Zhang
    • 1
    • 2
  • Feifei Xu
    • 2
  1. 1.Department of Computer ScienceUniversity of Regina, ReginaSaskatchewanCanada
  2. 2.Department of Computer Science and TechnologyTongji UniversityShanghaiChina

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