Skip to main content

Toward Rough Sets Based Rule Generation from Tables with Uncertain Numerical Values

  • Chapter
Integrated Uncertainty Management and Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

  • 932 Accesses

Abstract

Rough sets based rule generation from tables with uncertain numerical values is presented. We have already focused on two topics, i.e., rule generation from tables with non-deterministic information and rule generation from tables with numerical values. For non-deterministic information, we have extended the typical rough sets to rough sets based on uncertain information. For numerical values, we have defined numerical patterns with two symbols ’@’ and ’#’, and have introduced the equivalence classes depending upon the figures. This paper employs intervals for uncertain numerical values, as well as rules with intervals. By using a real example, we show that it is possible to handle such rules according to the same method as the one already developed for non-deterministic information.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: Proc. the 20th Very Large Data Base, pp. 487–499 (1994)

    Google Scholar 

  2. Ceglar, A., Roddick, J.F.: Association mining. ACM Comput. Surv. 38(2) (2006)

    Google Scholar 

  3. Chmielewski, M., Grzymala-Busse, J.: Global Discretization of Continuous Attributes as Preprocessing for Machine Learning. Int’l. J. Approximate Reasoning 15, 319–331 (1996)

    Article  MATH  Google Scholar 

  4. Cluster Analysis, http://en.wikipedia.org/wiki/Cluster_analysis

  5. Confidence Interval, http://en.wikipedia.org/wiki/Confidence_interval

  6. Grzymala-Busse, J.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. Transactions on Rough Sets 1, 78–95 (2004)

    Google Scholar 

  7. Grzymala-Busse, J., Stefanowski, J.: Three Discretization Methods for Rule Induction. Int’l. Journal of Intelligent Systems 16, 29–38 (2001)

    Article  MATH  Google Scholar 

  8. Infobright.org Forums, http://www.infobright.org/Forums/viewthread/288/ , http://www.infobright.org/Forums/viewthread/621/

  9. Kryszkiewicz, M.: Rules in Incomplete Information Systems. Information Sciences 113, 271–292 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Leung, Y., Fischer, M.M., Wu, W.Z., Mi, J.S.: A Rough Set Approach for the Discovery of Classification Rules in Interval-valued Information Systems. Int’l. J. Approximate Reasoning 47(2), 233–246 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lipski, W.: On Semantic Issues Connected with Incomplete Information Data Base. ACM Trans. DBS 4, 269–296 (1979)

    Google Scholar 

  12. Murai, T., Resconi, G., Nakata, M., Sato, Y.: Operations of Zooming In and Out on Possible Worlds for Semantic Fields. In: Knowledge-Based Intelligent Information Engineering Systems and Allied Technologies, pp. 1083–1087. IOS Press, Amsterdam (2002)

    Google Scholar 

  13. Orłowska, E., Pawlak, Z.: Representation of Nondeterministic Information. Theoretical Computer Science 29, 27–39 (1984)

    Article  MathSciNet  Google Scholar 

  14. Pawlak, Z.: Rough Sets. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  15. Quinlan, J.R.: Improved Use of Continuous Attributes in C4.5. Journal of Artificial Intelligence Research 4, 77–90 (1996)

    MATH  Google Scholar 

  16. Sakai, H., Okuma, A.: Basic Algorithms and Tools for Rough Non-deterministic Information Analysis. Transactions on Rough Sets 1, 209–231 (2004)

    Google Scholar 

  17. Sakai, H., Ishibashi, R., Nakata, M.: On Rules and Apriori Algorithm in Non-deterministic Information Systems. Transactions on Rough Sets 9, 328–350 (2008)

    Google Scholar 

  18. Sakai, H., Ishibashi, R., Nakata, M.: Lower and Upper Approximations of Rules in Non-deterministic Information Systems. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 299–309. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Sakai, H., Koba, K., Nakata, M.: Rough Sets Based Rule Generation from Data with Categorical and Numerical Values. Journal of Advanced Computational Intelligence and Intelligent Informatics 12(5), 426–434 (2008)

    Google Scholar 

  20. Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Intelligent Decision Support - Handbook of Advances and Applications of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  21. Ślȩzak, D., Sakai, H.: Automatic Extraction of Decision Rules from Non-deterministic Data Systems: Theoretical Foundations and SQL-Based Implementation. In: Proc. of DTA 2009. CCIS, vol. 64, pp. 151–162 (2009)

    Google Scholar 

  22. UCI Machine Learning Repository, http://mlearn.ics.uci.edu/MLRepository.html

  23. Van-Nam, H., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H. (eds.): Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol. 46. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  24. Van-Nam, H., Nakamori, Y., Hu, C., Kreinovich, V.: On Decision Making under Interval Uncertainty. In: Proc.39th International Symposium on Multiple-Valued Logic, pp. 214–220. IEEE Society, Los Alamitos (2009)

    Google Scholar 

  25. Yang, X., Yu, D., Jingyu, Y., Wei, L.: Dominance-based Rough Set Approach to Incomplete Interval-valued Information System. Data and Knowledge Engineering 68(11), 1331–1347 (2009)

    Article  Google Scholar 

  26. Yao, Y., Liau, C., Zhong, N.: Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 152–159. Springer, Heidelberg (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sakai, H., Nakata, M., Ślȩzak, D. (2010). Toward Rough Sets Based Rule Generation from Tables with Uncertain Numerical Values. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11960-6_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics