Nothing Special   »   [go: up one dir, main page]

Skip to main content

An Empirical Comparison of Rule Sets Induced by LERS and Probabilistic Rough Classification

  • Chapter
Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 42))

Abstract

We explore an extension of rough set theory based on probability theory. Lower and upper approximations, the basic ideas of rough set theory, are generalized by adding two parameters, denoted by alpha and beta. In our experiments, for different pairs of alpha and beta, we induced three types of rules: positive, boundary, and possible. The quality of these rules was evaluated using ten-fold cross-validation on five data sets. The main results of our experiments are that there is no significant difference in quality between positive and possible rules and that boundary rules are the worst.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Similar content being viewed by others

References

  1. Grzymała-Busse, J.W.: Knowledge acquisition under uncertainty–A rough set approach. Journal of Intelligent & Robotic Systems 1, 3–16 (1988)

    Article  Google Scholar 

  2. Grzymała-Busse, J.W.: LERS—a system for learning from examples based on rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  3. Grzymała-Busse, J.W.: MLEM2: A new algorithm for rule induction from imperfect data. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2002), pp. 243–250. ESIA- Université de Savoie, France (2002)

    Google Scholar 

  4. Grzymała-Busse, J.W., Marepally, S.R., Yao, Y.: A comparison of positive, boundary, and possible rules using the MLEM2 rule induction algorithm. In: Proceedings of the 10th International Conference on Hybrid Intelligent Systems, pp. 7–12. IEEE Computer Society Press, Washington, DC (2010)

    Chapter  Google Scholar 

  5. Grzymała-Busse, J.W., Yao, Y.: Probabilistic rule induction with the LERS data mining system. International Journal of Intelligent Systems 26, 518–539 (2011)

    Article  Google Scholar 

  6. Grzymała-Busse, J.W., Ziarko, W.: Data mining based on rough sets. In: Wang, J. (ed.) Data Mining: Opportunities and Challenges, pp. 142–173. Idea Group Publ., Hershey (2003)

    Google Scholar 

  7. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  9. Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)

    Article  MATH  Google Scholar 

  10. Stefanowski, J.: Algorithms of Decision Rule Induction in Data Mining. Poznań University of Technology Press, Poznań (2001)

    Google Scholar 

  11. Tsumoto, S.: Accuracy and Coverage in Rough Set Rule Induction. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 373–380. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Tsumoto, S., Tanaka, H.: PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods. Computational Intelligence 11, 389–405 (1995)

    Article  Google Scholar 

  13. Yao, Y.: Decision-Theoretic Rough Set Models. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślęzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180, 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  15. Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)

    Article  Google Scholar 

  16. Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Raś, Z., Zemankova, M., Emrich, M. (eds.) Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee, October 25-27, pp. 388–395. Elsevier Press (1990)

    Google Scholar 

  17. Yao, Y.Y., Zhong, N.: An Analysis of Quantitative Measures Associated with Rules. In: Zhong, N., Zhou, L. (eds.) PAKDD 1999. LNCS (LNAI), vol. 1574, pp. 479–488. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  18. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jerzy W. Grzymała-Busse .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Grzymała-Busse, J.W., Marepally, S.R., Yao, Y. (2013). An Empirical Comparison of Rule Sets Induced by LERS and Probabilistic Rough Classification. In: Skowron, A., Suraj, Z. (eds) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. Intelligent Systems Reference Library, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30344-9_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30344-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30343-2

  • Online ISBN: 978-3-642-30344-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics