A New Formulation of Multi-category Decision-Theoretic Rough Sets

  • Bing Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6954)

Abstract

As a natural extension to the rough set approximations with two decision classes, this paper provides a new formulation of multi-category decision-theoretic rough sets. A three-way decision is added to each class which gives the user the flexibility of making a deferred decision. Different misclassification errors are treated separately with the notion of loss functions from Bayesian decision theory. The losses incurred for making deferred and rejective decisions to each class are also considered. The main objective of this paper is to tackle the limitations of the previous related work, and therefore provide a more complete solution to multi-category decision making.

Keywords

Multi-category classification probabilistic approximation three-way decision Bayesian decision Theory rough sets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)MATHGoogle Scholar
  2. 2.
    Herbert, J.P., Yao, J.T.: Game-theoretic risk analysis in decision-theoretic rough sets. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 132–139. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Lingras, P., Chen, M., Miao, D.Q.: Rough multi-category decision theoretic framework. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 676–683. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Liu, D., Li, T.R., Hu, P., Li, H.X.: Multiple-category classification with decision-theoretic rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS(LNAI), vol. 6401, pp. 703–710. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)MATHGoogle Scholar
  6. 6.
    Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)CrossRefMATHGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)CrossRefGoogle Scholar
  9. 9.
    Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)CrossRefMATHGoogle Scholar
  10. 10.
    Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180, 341–353 (2010)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Information Sciences 181, 1080–1096 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)CrossRefGoogle Scholar
  13. 13.
    Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Information Sciences 178, 3356–3373 (2008)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Yao, Y.Y., Zhou, B.: Naive bayesian rough sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS(LNAI), vol. 6401, pp. 719–726. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Zhou, B., Yao, Y.Y., Luo, J.G.: A three-way decision approach to email spam filtering. In: Farzindar, A., Kešelj, V. (eds.) Canadian AI 2010. LNCS(LNAI), vol. 6085, pp. 28–39. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Ziarko, W.: Variable precision rough sets model. Journal of Computer and Systems Sciences 46, 39–59 (1993)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bing Zhou
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

Personalised recommendations