Granular Structures and Approximations in Rough Sets and Knowledge Spaces

  • Yiyu Yao
  • Duoqian Miao
  • Feifei Xu
Part of the Studies in Computational Intelligence book series (SCI, volume 174)


Multilevel granular structures play a fundamental role in granular computing. In this chapter, we present a general framework of granular spaces. Within the framework, we examine the granular structures and approximations in rough set analysis and knowledge spaces. Although the two theories use different types of granules, they can be unified in the proposed framework.


Knowledge Structure Atomic Formula Granular Structure Knowledge State Formal Concept Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)Google Scholar
  2. 2.
    Bargiela, A., Pedrycz, W.: Toward a theory of granular computing for human-centred information processing. IEEE Transactions On Fuzzy Systems (to appear)Google Scholar
  3. 3.
    Doignon, J.P., Falmagne, J.C.: Spaces for the assessment of knowledge. International Journal of Man-Machine Studies 23, 175–196 (1985)zbMATHCrossRefGoogle Scholar
  4. 4.
    Doignon, J.P., Falmagne, J.C.: Knowledge spaces. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  5. 5.
    Duntsch, I., Gediga, G.: A note on the correspondences among entail relations, rough set dependencies, and logical consequence. Mathematical Psychology 43, 393–401 (2001)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Falmagne, J.C., Koppen, M., Villano, M., Doignon, J.P., Johanessen, L.: Introduction to knowledge spaces: how to test and search them. Psychological Review 97, 201–224 (1990)CrossRefGoogle Scholar
  7. 7.
    Lin, T.Y., Yao, Y.Y., Zadeh, L.A.: Data Mining, Rough Sets and Granular Computing. Physica-Verlag, Heidelberg (2002)zbMATHGoogle Scholar
  8. 8.
    Nguyen, S.H., Skowron, A., Stepaniuk, J.: Granular computing: a rough set approach. Computational Intelligence 17, 514–544 (2001)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Orlowska, E.: Logical aspects of learning concepts. International Journal of Approximate Reasoning 2, 349–364 (1988)zbMATHCrossRefGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pawlak, Z.: Rough Sets. In: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)Google Scholar
  12. 12.
    Pinker, S.: How the mind works. Norton, New York (1997)Google Scholar
  13. 13.
    Polkowski, L., Semeniuk-Polkowska, M.: On foundations and applications of the paradigm of granular rough computing. International Journal of Cognitive Informatics and Natural Intelligence 2, 80–94 (2008)Google Scholar
  14. 14.
    Simon, H.A.: The Sciences of the Artificial. MIT Press, Cambridge (1996)Google Scholar
  15. 15.
    Solso, R.L., Maclin, M.K., Maclin, O.H.: Cognitive psychology. Allyn and Bacon, Boston (2005)Google Scholar
  16. 16.
    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.) Foundations of Intelligent Systems. LNCS, vol. 4994, pp. 319–328. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Yao, J.T.: A ten-year review of granular computing. In: Proceedings of 2007 IEEE International Conference on Granular Computing, pp. 734–739 (2007)Google Scholar
  18. 18.
    Yao, Y.Y.: On generalizing rough set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS, vol. 2639, pp. 44–51. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Yao, Y.Y.: A partition model of granular computing. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)Google Scholar
  20. 20.
    Yao, Y.Y.: Granular computing. Computer Science (Ji Suan Ji Ke Xue).  31, 1–5 (2004)Google Scholar
  21. 21.
    Yao, Y.Y.: Perspectives of granular computing. In: Proceedings of 2005 IEEE International Conference on Granular Computing, pp. 85–90 (2005)Google Scholar
  22. 22.
    Yao, Y.Y.: Three perspectives of granular computing. Journal of Nanchang Institute of Technology 25(2), 16–21 (2006)Google Scholar
  23. 23.
    Yao, Y.Y.: A note on definability and approximations. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII. LNCS, vol. 4400, pp. 274–282. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Yao, Y.Y.: The art of granular computing. In: Proceeding of the International Conference on Rough Sets and Emerging Intelligent Systems Paradigms, pp. 101–112 (2007)Google Scholar
  25. 25.
    Yao, Y.Y.: The rise of granular computing. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition) 20(3), 1–10 (2008)Google Scholar
  26. 26.
    Yao, Y.Y., Chen, Y.H.: Rough set approximations in formal concept analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 285–305. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing 2, 103–120 (1996)Google Scholar
  28. 28.
    Yao, Y.Y., Zhou, B.: A logic language of granular computing. In: Proceedings 6th IEEE International Conference on Cognitive Informatics, pp. 178–185 (2006)Google Scholar
  29. 29.
    Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 111–127 (1997)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yiyu Yao
    • 1
  • Duoqian Miao
    • 2
  • Feifei Xu
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada
  2. 2.Department of Computer Science and TechnologyTongji UniversityShanghaiChina

Personalised recommendations