Skip to main content
SpringerLink
Log in

Comparison of Two Models of Probabilistic Rough Sets

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8171))

Included in the following conference series:

Abstract

To generalize the classical rough set model, several proposals have been made by considering probabilistic information. Each of the proposed probabilistic models uses three regions for approximating a concept. Although the three regions are similar in form, they have different semantics and therefore are appropriate for different applications. In this paper, we present a comparative study of a decision-theoretic rough set model and a confirmation-theoretic rough set model. We argue that the former deals with drawing conclusions based on available evidence and the latter concerns evaluating difference pieces of evidence. By considering both models, we can obtain a more comprehensive understanding of probabilistic rough sets.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Azam, N., Yao, J.T.: Multiple criteria decision analysis with game-theoretic rough sets. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 399–408. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Bayes, T., Price, R.: An essay towards solving a problem in the doctrine of chance. Philosophical Transactions of the Royal Society of London 53, 370–418 (1763)

    Google Scholar 

  3. Dembczyński, K., Greco, S., Kotłowski, W., Słowiński, R.: Statistical model for rough set approach to multicriteria classification. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702, pp. 164–175. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Deng, X., Yao, Y.Y.: An information-theoretic interpretation of thresholds in probabilistic rough sets. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 369–378. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Festa, R.: Bayesian Confirmation. In: Galavotti, M., Pagnini, A. (eds.) Experience, Reality, and Scientific Explanation, pp. 55–87. Kluwer Academic Publishers, Dordrecht (1999)

    Chapter  Google Scholar 

  6. Fitelson, B.: Studies in Bayesian Confirmation Theory. Ph.D. Dissertation, University of Wisconsin (2001), http://fitelson.org/thesis.pdf

  7. Greco, S., Pawlak, Z., Słowiński, R.: Bayesian confirmation measures within rough set approach. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 264–273. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Greco, S., Matarazzo, B., Słowiński, R.: Rough membership and Bayesian confirmation measures for parameterized rough sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 314–324. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Greco, S., Matarazzo, B., Słowiński, R.: Parameterized rough set model using rough membership and Bayesian confirmation measures. International Journal of Approximate Reasoning 49, 285–300 (2009)

    Article  Google Scholar 

  10. Grzymala-Busse, J.W.: Generalized probabilistic approximations. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 1–16. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  12. Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundamenta Informaticae 108, 267–286 (2011)

    MathSciNet  MATH  Google Scholar 

  13. Jia, X.Y., Liao, W.H., Tang, Z.M., Shang, L.: Minimum cost attribute reduction in decision-theoretic rough set models. Information Sciences 219, 151–167 (2013)

    Article  MathSciNet  Google Scholar 

  14. Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: A three-way view decision model. International Journal of Computational Intelligence Systems 4, 1–11 (2011)

    Google Scholar 

  15. Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decision-theoretic rough sets for classifications. International Journal of Approximate Reasoning (2013), http://dx.doi.org/10.1016/j.ijar.2013.02.013

  16. Liu, D., Li, T.R., Ruan, D.: Probabilistic model criteria with decision-theoretic rough sets. Information Science 181, 3709–3722 (2011)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  18. Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, John Wiley and Sons, New York, pp. 251–271. John Wiley and Sons, Chichester (1994)

    Google Scholar 

  19. 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 

  20. Ślęzak, D.: Rough sets and Bayes factor. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 202–229. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Ślęzak, D., Ziarko, W.: Bayesian rough set model. Proceedings of FDM 2002, pp. 131–135 (2002)

    Google Scholar 

  22. Ślęzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wong, S.K.M., Ziarko, W.: A probabilistic model of approximate classification and decision rules with uncertainty in inductive learning. Technical Report CS-85-23, Department of Computer Science, University of Regina (1985)

    Google Scholar 

  24. Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)

    Article  Google Scholar 

  25. Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximation Reasoning 49, 255–271 (2008)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  27. Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Information Sciences 181, 1080–1096 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Yao, Y.Y.: Two semantic issues in a probabilistic rough set model. Fundamenta Informaticae 108, 249–265 (2011)

    MathSciNet  MATH  Google Scholar 

  29. Yao, Y.Y.: An outline of a theory of three-way decisions. In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 1–17. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  31. Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–24. North-Holland, Amsterdam (1990)

    Google Scholar 

  32. Yao, Y.Y., Zhou, B.: Naive Bayesian rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS, vol. 6401, pp. 719–726. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  33. Ziarko, W.: Variable precision rough sets model. Journal of Computer and Systems Sciences 46, 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Sam Houston State University, Huntsville, Texas, USA, 77340

    Bing Zhou

  2. Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada, S4S 0A2

    Yiyu Yao

Authors
  1. Bing Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yiyu Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  2. Maria Curie-Skłodowska University, Lublin, Poland

    Marcin Wolski

  3. University of Granada, Spain

    Chris Cornelis

  4. Indian Statistical Institute, 700108, Kolkata, India

    Sushmita Mitra

  5. University of Warsaw, 02-097, Warsaw, Poland

    Piotr Wasilewski

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhou, B., Yao, Y. (2013). Comparison of Two Models of Probabilistic Rough Sets. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41299-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41298-1

  • Online ISBN: 978-3-642-41299-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation