Skip to main content

Risk Assessment in Granular Environments

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6499))

Abstract

We discuss the problem of measuring the quality of decision support (classification) system that involves granularity. We put forward the proposal for such quality measure in the case when the underlying granular system is based on rough and fuzzy set paradigms. We introduce the notion of approximation, loss function, and empirical risk functional that are inspired by empirical risk assessment for classifiers in the field of statistical learning.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Warwick, B. (ed.): The Handbook of Risk. John Wiley & Sons, New York (2003)

    Google Scholar 

  2. Bostrom, A., French, S., Gottlieb, S. (eds.): Risk Assessment, Modeling and Decision Support. Risk, Governance and Society, vol. 14. Springer, Heidelberg (2008)

    Google Scholar 

  3. Vapnik, V.: Statisctical Learning Theory. John Wiley & Sons, New York (1998)

    Google Scholar 

  4. Berger, J.O.: Statistical Decision Theory and Bayesian Analysis, 2nd edn. Springer, New York (1985)

    Book  MATH  Google Scholar 

  5. Szczuka, M.: Towards approximation of risk. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 320–328. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Szczuka, M.S.: Approximation of loss and risk in selected granular systems. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Slezak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 168–175. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Skowron, A., Szczuka, M.S.: Toward interactive computations: A rough-granular approach. In: Advances in Machine Learning II. SCI, vol. 263, pp. 23–42. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons, New York (2007)

    Google Scholar 

  9. Zadeh, L.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Application, pp. 3–18. North-Holland Publishing Co., Amsterdam (1979)

    Google Scholar 

  10. Vapnik, V.: Principles of risk minimization for learning theory. In: Proceedings of NIPS, pp. 831–838 (1991)

    Google Scholar 

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

    MATH  Google Scholar 

  12. Pawlak, Z.: Rough sets, rough functions and rough calculus. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in and Decision Making, pp. 99–109. Springer, Singapore (1999)

    Google Scholar 

  13. Halmos, P.: Measure Theory. Springer, Berlin (1974)

    MATH  Google Scholar 

  14. Höeppner, F., Klawonn, F.: Systems of information granules. In: [8], pp. 187–203

    Google Scholar 

  15. Yager, R.R., Filev, D.P.: Essentials of fuzzy modeling and control. John Wiley & Sons, Chichester (1994)

    Google Scholar 

  16. Skowron, A., Synak, P.: Complex patterns. Fundamenta Informaticae 60(1-4), 351–366 (2004)

    MathSciNet  MATH  Google Scholar 

  17. Jankowski, A., Peters, J.F., Skowron, A., Stepaniuk, J.: Optimization in discovery of compound granules. Fundamenta Informaticae 85, 249–265 (2008)

    MathSciNet  MATH  Google Scholar 

  18. Kleinberg, J., Papadimitriou, C., Raghavan, P.: A microeconomic view of data mining. Data Mining and Knowledge Discovery 2, 311–324 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Szczuka, M. (2011). Risk Assessment in Granular Environments. In: Peters, J.F., Skowron, A., Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Transactions on Rough Sets XIII. Lecture Notes in Computer Science, vol 6499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18302-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-18302-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18301-0

  • Online ISBN: 978-3-642-18302-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics