Advertisement

Monotonic Uncertainty Measures in Probabilistic Rough Set Model

  • Guoyin Wang
  • Xi’ao Ma
  • Hong Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8537)

Abstract

Uncertainty measure is one of the key research issues in the rough set theory. In the Pawlak rough set model, the accuracy measure, the roughness measure and the approximation accuracy measure are used as uncertainty measures. Monotonicity is a basic property of these measures. However, the monotonicity of these measures does not hold in the probabilistic rough set model, which makes them not so reasonable to evaluate the uncertainty. The main objective of this paper is to address the uncertainty measure problem in the probabilistic rough set model. We propose three monotonic uncertainty measures which are called the probabilistic accuracy measure, the probabilistic roughness measure and the probabilistic approximation accuracy measure respectively. The monotonicity of the proposed uncertainty measures is proved to be held. Finally, an example is used to verify the validity of the proposed uncertainty measures.

Keywords

Uncertainty measures approximation accuracy Pawlak rough set model probabilistic rough set model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dai, J.H., Wang, W.T., Xu, Q.: An uncertainty measure for incomplete decision tables and its applications. IEEE Transactions on Cybernetics 43, 1277–1289 (2012)CrossRefGoogle Scholar
  2. 2.
    Dai, J.H., Xu, Q.: Approximations and uncertainty measures in incomplete information systems. Information Sciences 198, 62–80 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hu, Q.H., Zhang, L., Chen, D.G., Pedrycz, W., Yu, D.R.: Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications. International Journal of Approximate Reasoning 51(4), 453–471 (2010)CrossRefGoogle Scholar
  4. 4.
    Katzberg, J.D., Ziarko, W.: Variable precision rough sets with asymmetric bounds. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 167–177. Springer, London (1994)CrossRefGoogle Scholar
  5. 5.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)CrossRefGoogle Scholar
  6. 6.
    Pawlak, Z.: Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston (1991)CrossRefGoogle Scholar
  7. 7.
    Qian, Y.H., Liang, J.Y., Wang, F.: A new method for measuring the uncertainty in incomplete information systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17(06), 855–880 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Shen, Q., Jensen, R.: Rough sets, their extensions and applications. International Journal of Automation and Computing 4, 217–228 (2007)CrossRefGoogle Scholar
  9. 9.
    Xu, W.H., Zhang, X.Y., Zhang, W.X.: Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems. Applied Soft Computing 9(4), 1244–1251 (2009)CrossRefGoogle Scholar
  10. 10.
    Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Guoyin Wang
    • 1
  • Xi’ao Ma
    • 1
    • 2
  • Hong Yu
    • 1
  1. 1.Chongqing Key Laboratory of Computational IntelligenceChongqing University of Posts and TelecommunicationsChongqingChina
  2. 2.School of Information Science and TechnologySouthwest Jiaotong UniversityChengduChina

Personalised recommendations