Skip to main content
SpringerLink
Log in

Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets

  • Conference paper
Book cover Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3641))

Abstract

A generalization of the original idea of rough sets and variable precision rough sets is introduced. This generalization is based on the concept of absolute and relative rough membership. Similarly to variable precision rough set model, the generalization called parameterized rough set model, is aimed at modeling data relationships expressed in terms of frequency distribution rather than in terms of a full inclusion relation used in the classical rough set approach. However, differently from variable precision rough set model, one or more parameters modeling the degree to which the condition attribute values confirm the decision attribute value, are considered. The properties of this extended model are investigated and compared to the classical rough set model and the variable precision rough set model.

The research of the first two authors has been supported by the Italian Ministry of Education, University and Scientific Research (MIUR). The third author wishes to acknowledge financial support from the State Committee for Scientific Research (KBN).

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Eells, E., Fitelson, B.: Symmetries and assymetries in evidential support. Philosophical Studies 107, 129–142 (2002)

    Article  Google Scholar 

  2. Fitelson, B.: Studies in Bayesian Confirmation Theory. Ph.D. thesis, University of Wisconsin-Madison (2001)

    Google Scholar 

  3. Greco, S., Pawlak, Z., Słowiński, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Engineering Applications of Artificial Intelligence 17, 345–361 (2004)

    Article  Google Scholar 

  4. Hilderman, R.J., Hamilton, H.J.: Knowledge Discovery and Measures of Interest. Kluwer Academic Publishers, Boston (2001)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Pawlak, Z.: Rough Sets. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  7. Pawlak, Z.: Rough Sets, decision algorithms and Bayes’ Theorem. European Journal of Operational Research 136, 181–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  9. Popper, K.R.: The Logic of Scientific Discovery, Hutchinson, London (1959)

    Google Scholar 

  10. 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 

  11. Ślȩzak, D., Ziarko, W.: Bayesian rough set model. In: Proc. of Intl. Conference on Data Mining. Foundations of Data Mining and Knowledge Discovery Workshop, Meabashi City, Japan, pp. 131–136 (2002)

    Google Scholar 

  12. 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 

  13. Ziarko, W.: Variable precision Rough Sets Model. Journal of Computer and System Science 46(1), 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ziarko, W.: Variable precision rough sets with asymmetric bounds. In: Ziarko, W. (ed.) Rough sets, Fuzzy sets and Knowledge Discovery, pp. 167–177. Springer, Berlin (1994)

    Google Scholar 

  15. Ziarko, W.: Set approximation quality measures in the variable precision rough set model. In: Soft Computing Systems, Management and Applications, pp. 442–452. IOS Press, Amsterdam (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo

  2. Institute of Computing Science, Poznań University of Technology, 60-965, Poznań

    Roman Słowiński

  3. Institute for Systems Research, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

Authors
  1. Salvatore Greco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benedetto Matarazzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roman Słowiński
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2 Canada, Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, P.O. Box, Poland

    Dominik Ślęzak

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Guoyin Wang

  3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Marcin Szczuka

  4. Department of Computer Science, Brock University, St. Catharines, L2S 3A1, Ontario, Canada

    Ivo Düntsch

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

    Yiyu Yao

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Greco, S., Matarazzo, B., Słowiński, R. (2005). Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_33

Download citation

  • DOI: https://doi.org/10.1007/11548669_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28653-0

  • Online ISBN: 978-3-540-31825-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation