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

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Rough Sets and Knowledge Technology (RSKT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6954))

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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.

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References

  1. Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. 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 

  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)

    Article  Google Scholar 

  13. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Information Sciences 178, 3356–3373 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Zhou, B. (2011). A New Formulation of Multi-category Decision-Theoretic Rough Sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_66

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  • DOI: https://doi.org/10.1007/978-3-642-24425-4_66

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24424-7

  • Online ISBN: 978-3-642-24425-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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