Representation and Evaluation of Granular Systems

Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 15)

Abstract

We put forward a general framework for looking at the quality of granular systems. We discuss issues of representing and using granular methods in comparison with traditional approach. We focus on the demand for quality evaluation strategies that judge granular environments by their ability to reduce computational effort and simplify description, assuring required level of precision and relevance at the same time. We provide several examples to illustrate our approach.

Keywords

Query Processing Empirical Risk Granular System Granulate Information Granular Computing 
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.

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References

  1. 1.
    Aggarwal, C.C. (ed.): Data Streams - Models and Algorithms. Advances in Database Systems, vol. 31. Springer (2007)Google Scholar
  2. 2.
    Apolloni, B., Pedrycz, W., Bassis, S., Malchiodi, D.: The Puzzle of Granular Computing. SCI, vol. 138. Springer (2008)Google Scholar
  3. 3.
    Beaubouef, T., Petry, F.E.: Uncertainty Modeling for Database Design Using Intuitionistic and Rough Set Theory. Journal of Intelligent and Fuzzy Systems 20(3), 105–117 (2009)MATHGoogle Scholar
  4. 4.
    Bembenik, R., Skonieczny, Ł., Rybiński, H., Niezgódka, M. (eds.): Intelligent Tools for Building a Scientific Information Platform. SCI, vol. 390. Springer (in print, 2012)Google Scholar
  5. 5.
    Chaudhuri, S., Narasayya, V.R.: Self-tuning database systems: A decade of progress. In: Koch, C., Gehrke, J., Garofalakis, M.N., Srivastava, D., Aberer, K., Deshpande, A., Florescu, D., Chan, C.Y., Ganti, V., Kanne, C.C., Klas, W., Neuhold, E.J. (eds.) VLDB, pp. 3–14. ACM (2007)Google Scholar
  6. 6.
    Dorneles, C.F., Goncalves, R., dos Santos Mello, R.: Approximate data instance matching: a survey. Knowl. Inf. Syst. 27, 1–21 (2011), doi: http://dx.doi.org/10.1007/s10115-010-0285-0 CrossRefGoogle Scholar
  7. 7.
    Guillet, F., Hamilton, H.J. (eds.): Quality Measures in Data Mining. SCI, vol. 43. Springer (2007)Google Scholar
  8. 8.
    Guyon, I., Elisseeff, A.: An Introduction to Variable and Feature Selection. Journal of Machine Learning Research 3, 1157–1182 (2003)MATHGoogle Scholar
  9. 9.
    Idreos, S., Manegold, S., Kuno, H.A., Graefe, G.: Merging what’s cracked, cracking what’s merged: Adaptive indexing in main-memory column-stores. PVLDB 4(9), 585–597 (2011)Google Scholar
  10. 10.
    Kreinovich, V.: Towards Faster Estimation of Statistics and ODEs Under Interval, P-Box, and Fuzzy Uncertainty: From Interval Computations to Rough Set-Related Computations. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds.) RSFDGrC 2011. LNCS (LNAI), vol. 6743, pp. 3–10. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Nguyen, H.S.: Approximate Boolean Reasoning: Foundations and Applications in Data Mining. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 334–506. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Pawlak, Z., Skowron, A.: Rudiments of Rough Sets. Information Sciences 177(1), 3–27 (2007)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Pedrycz, W.: The Principle of Justifiable Granularity and an Optimization of Information Granularity Allocation as Fundamentals of Granular Computing. Journal of Information Processing Systems 7(3), 397–412 (2011)CrossRefGoogle Scholar
  14. 14.
    Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons (2008)Google Scholar
  15. 15.
    Sakai, H., Ishibashi, R., Koba, K., Nakata, M.: Rules and Apriori Algorithm in Non-deterministic Information Systems. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 328–350. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Ślęzak, D., Janusz, A.: Ensembles of Bireducts: Towards Robust Classification and Simple Representation. In: Kim, T.-h., Adeli, H., Slezak, D., Sandnes, F.E., Song, X., Chung, K.-i., Arnett, K.P. (eds.) FGIT 2011. LNCS, vol. 7105, pp. 64–77. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Ślęzak, D., Kowalski, M.: Intelligent Data Granulation on Load: Improving Infobright’s Knowledge Grid. In: Lee, Y.-h., Kim, T.-h., Fang, W.-c., Ślęzak, D. (eds.) FGIT 2009. LNCS, vol. 5899, pp. 12–25. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Szczuka, M.: Risk Assessment in Granular Environments. In: Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) Transactions on Rough Sets XIII. LNCS, vol. 6499, pp. 121–134. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Szczuka, M.S., Skowron, A., Stepaniuk, J.: Function Approximation and Quality Measures in Rough-Granular Systems. Fundamenta Informaticae 109(3), 339–354 (2011)MathSciNetMATHGoogle Scholar
  20. 20.
    Szczuka, M.S., Ślęzak, D.: Feedforward Neural Networks for Compound Signals. Theoretical Computer Science 412(42), 5960–5973 (2011)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Vapnik, V.: Statistical Learning Theory. John Wiley & Sons (1998)Google Scholar
  22. 22.
    Zadeh, L.A.: Toward a Generalized Theory of Uncertainty (GTU) - An Outline. Information Sciences 172(1-2), 1–40 (2005)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of MathematicsThe University of WarsawWarsawPoland
  2. 2.Infobright Inc.WarsawPoland

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