Advertisement

Granular Concept Mapping and Applications

  • Sumalee SonamthiangEmail author
  • Kanlaya Naruedomkul
  • Nick Cercone
Part of the Intelligent Systems Reference Library book series (ISRL, volume 42)

Abstract

This chapter presents a granular concept hierarchy (GCH) construction and mapping of the hierarchy for granular knowledge. A GCH is comprised of multilevel granular concepts with their hierarchy relations. A rough set based approach is proposed to induce the approximation of a domain concept hierarchy of an information system. A sequence of attribute subsets is selected to partition a granularity, hierarchically. In each level of granulation, reducts and core are applied to retain the specific concepts of a granule whereas common attributes are applied to exclude the common knowledge and generate a more general concept. A granule description language and granule measurements are proposed to enable mapping for an appropriate granular concept that represents sufficient knowledge so solve problem at hand. Applications of GCH are demonstrated through learning of higher order decision rules.

Keywords

Information granules granular knowledge granular concept hierarchy granular knowledge mapping granule description language higher-order rules multilevel partitioning attribute selection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bargiela, A., Pedrycz, W.: Granular Computing. An introduction. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  2. 2.
    Bargiela, A., Pedrycz, W.: Toward a theory of granular computing for human-centered information processing. IEEE Transactions on Fuzzy Systems 16(2), 320–330 (2008)CrossRefGoogle Scholar
  3. 3.
    Bazan, J.G., Szczuka, M.S.: The Rough Set Exploration System. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 37–56. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Biswas, G., Weinberg, J.B., Fisher, D.H.: ITERATE: a conceptual clustering algorithm for data mining. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews 28(2), 219–230 (1998)CrossRefGoogle Scholar
  5. 5.
    Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis. LNCS (LNAI), vol. 3626. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Grzymała-Busse, J.W., Siddhaye, S.: Rough set approaches to rule induction from incomplete data. In: Proceedings of the 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2004, Perugia, Italy, July 4-9, vol. 2, pp. 923–930 (2004)Google Scholar
  7. 7.
    Hoa, N.S., Son, N.H.: Rough set approach to approximation of concepts from taxonomy. In: Proc. of Knowledge Discovery and Ontologies Workshop, KDO 2004 at ECML/PKDD 2004, pp. 13–24 (2004)Google Scholar
  8. 8.
    Hu, X., Cercone, N.: Learning in relational databases: A rough set approach. J. Computational Intelligence 2, 323–337 (1995)CrossRefGoogle Scholar
  9. 9.
    Li, J., Cercone, N.J.: A Rough Set Based Model to Rank the Importance of Association Rules. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.) RSFDGrC 2005, Part II. LNCS (LNAI), vol. 3642, pp. 109–118. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11(5), 341–356 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Pawlak, Z.: Rough Sets. In: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)zbMATHCrossRefGoogle Scholar
  12. 12.
    Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Pawlak, Z., Skowron, A.: Rough sets: some extensions. Information Sciences 177(1), 28–40 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Information Sciences 177(1), 41–73 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley (2008)Google Scholar
  16. 16.
    Pedrycz, W., Vukovich, G.: Granular computing with shadowed sets. International Journal of Intelligent Systems 17, 173–197 (2002)zbMATHCrossRefGoogle Scholar
  17. 17.
    Pedrycz, W.: Shadowed sets: Representing and processing fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 28(1), 103–109 (1998)CrossRefGoogle Scholar
  18. 18.
    Peters, J.: Approximation and perception in ethology-based reinforcement learning. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Granular Computing, pp. 671–688. John Wiley & Sons, Ltd., Chichester (2008)CrossRefGoogle Scholar
  19. 19.
    Peters, J.: Near Sets. special Theory about Nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Priss, U.: Formal Concept Analysis in Information Science. In: Cronin, B. (ed.) Annual Review of Information Science and Technology, vol. 40, pp. 521–543. Information Today, Inc. on behalf of ASIS&T, Medford (2006)Google Scholar
  21. 21.
    Skowron, A., Peters, J.: Rough-granular computing. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Granular Computing, pp. 225–328. John Wiley & Sons, Ltd., Chichester (2008)Google Scholar
  22. 22.
    Tsumoto, S., Tanaka, H.: Discovery of Approximate Medical Knowledge Based on Rough Set Model. In: Żytkow, J.M. (ed.) PKDD 1998. LNCS, vol. 1510, pp. 468–476. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  23. 23.
    Yao, Y.Y.: Granular computing using neighborhood systems. In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing: Engineering Design and Manufacturing, The 3rd On-line World Conference on Soft Computing, WSC3, June 21-30, pp. 539–553. Springer, London (1999)Google Scholar
  24. 24.
    Yao, Y.Y.: Information Granulation and Rough Set Approximation. International Journal of Information Systems 16, 87–104 (2001)zbMATHGoogle Scholar
  25. 25.
    Yao, Y. Y., Yao, J.T.: Granular Computing as a Basis for Consistent Classification Problems. In: Proceedings of PAKDD 2002 Workshop on Toward the Foundation of Data Mining, pp. 101–106 (2002)Google Scholar
  26. 26.
    Yao, Y.Y.: Mining high order decision rules. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.) Rough Set Theory and Granular Computing, pp. 125–135. Springer, Berlin (2003)Google Scholar
  27. 27.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sumalee Sonamthiang
    • 1
    Email author
  • Kanlaya Naruedomkul
    • 2
  • Nick Cercone
    • 3
  1. 1.Institute for Innovative LearningMahidol UniversityNakhon PathomThailand
  2. 2.Mathematics Department, Faculty of ScienceMahidol UniversityBangkokThailand
  3. 3.Department of Computer Science and Engineering, Faculty of Science and EngineeringYork UniversityTorontoCanada

Personalised recommendations