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Dominance-based Rough Sets in “*” Incomplete Information System

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Incomplete Information System and Rough Set Theory

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Abstract

Dominance-based rough set approach is a very important expansion of Pawlak’s rough set approach since the former takes the preference-ordered domains of the attributes into account. In this chapter, the dominance-based rough set approach is introduced into the incomplete information system, in which all unknown values can be compared with any other values in the domains of the corresponding attributes. The “↑” and “↓” descriptors are employed to generate all certain rules from the incomplete information system. Moreover, the expanded dominance relation is also compared with the limited dominance relation, from which we can conclude that the limited dominance-based rough set approach is more suitable than the expanded dominance-based rough set approach when dealing with the incomplete information system.

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References

  1. Greco, S.,_Inuiguchi, M., Sŀowiński, R.: Fuzzy rough sets and multiple-premise gradual decision rules. Int. J. Approx. Reason. 41, 179–211 (2006)

    Article  MATH  Google Scholar 

  2. Greco, S., Matarazzo, B., Sŀowiński, R.: Handing missing values in rough set analysis of mutiattribute and muti-criteria decision problems. In: 7th International Workshop on New Directions in Rough Sets, Data Mining and Granular—Soft Computing, pp. 146–157 (1999)

    Google Scholar 

  3. Greco, S., Matarazzo, B., Sŀowiński, R.: Rough approximation by dominance relations. Int. J. Intell. Syst. 17, 153–171 (2002)

    Article  MATH  Google Scholar 

  4. Greco, S., Matarazzo, B., Sŀowiński, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1–47 (2002)

    Article  Google Scholar 

  5. Greco, S., Matarazzo, B., Sŀowiński, R.: Dominance-based rough set approach to case-Based reasoning. In: Third International Conference on Modeling Decisions for Artificial Intelligence, pp. 7–18 (2006)

    Google Scholar 

  6. Greco, S., Matarazzo, B., Sŀowiński, R.: Fuzzy set extensions of the dominance-based rough set approach. In: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, pp. 239–261 (2008)

    Google Scholar 

  7. Greco, S., Sŀowiński, R., Yao, Y. Y.: Bayesian decision theory for dominance-based rough set approach. In: The Second International Conference on Rough Sets and Knowledge Technology, pp. 143–141 (2007)

    Google Scholar 

  8. Bŀaszczyński, J., Greco, S., Sŀowiński, R.: On variable consistency dominance-based rough set approaches. In: The Fifth International Conference on Rough Sets and Current Trends in Computing, pp. 191–202 (2006)

    Google Scholar 

  9. Bŀaszczyński, J., Greco, S., Sŀowiński, R.: Monotonic variable consistency rough set approaches. In: Second International Conference on Rough Sets and Knowledge Technology, pp. 126–133 (2007)

    Google Scholar 

  10. Bŀaszczyński, J., Greco, S., Sŀowiński, R.: Multi-criteria classification—A new scheme for application of dominance-based decision rules. Eur. J. Oper. Res. 181, 1030–1044 (2007)

    Article  Google Scholar 

  11. Bŀaszczyński, J., Greco, S., Sŀowiński, R., Szeląg, M.: Monotonic variable consistency rough set approaches. Int. J. Approx. Reason. 50, 979–999 (2009)

    Article  MATH  Google Scholar 

  12. Dembczyński, K., Greco, S., Sŀowiński, R.: Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur. J. Oper. Res. 198, 626–636 (2009)

    Article  MATH  Google Scholar 

  13. Dembczyński, K., Pindur R.: Susmaga, R.: Dominance-based rough set classifier without induction of decision rules. Electronic Notes in Theoretical Computer Science 82 84–95 (2003)

    Article  Google Scholar 

  14. Qian, Y. H., Liang, J. Y., Dang, C. Y.: Interval ordered information systems. Comput. Math. Appl. 56, 1994–2009 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yang, X. B., Yu, D. J., Yang, J. Y., Wei, L. H.: Dominance-based rough set approach to incomplete interval-valued information system. Data Knowl. Eng. 68, 1331–1347 (2009)

    Article  Google Scholar 

  16. Fan, T. F., Liu, D. R., Tzeng, G. H.: Rough set-based logics for multicriteria decision analysis. Eur. J. Oper. Res. 182, 340–355 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hu, Q. H., Yu, D. R.: Variable precision dominance based rough set model and reduction algorithm for preference-ordered data. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 26–29 (2004)

    Google Scholar 

  18. Hu, Q. H., Yu, D. R., Guo, M. Z.: Fuzzy preference based rough sets. Inform. Sci. 180, 2003–2022 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hu, Q. H., Zhang, L., Chen, D. G., Pedrycz, W., Yu, D. R.: Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications. Int. J. Approx. Reason. 51, 453–471 (2010)

    Article  MATH  Google Scholar 

  20. Inuiguchi, M., Yoshioka, Y., Kusunoki, Y.: Variable-precision dominance-based rough set approach and attribute reduction. Int. J. Approx. Reason. 20, 1199–1214 (2009)

    Article  MathSciNet  Google Scholar 

  21. Kotlwski, W., Dembczyński, K., Greco, S., Sŀowiński, R.: Stochastic dominance-based rough set model for ordinal classification. Inform. Sci. 178, 4019–4037 (2008)

    Article  MathSciNet  Google Scholar 

  22. Shao, M. W., Zhang, W. X.: Dominance relation and rules in an incomplete ordered information system. Int. J. Intell. Syst. 20, 13–27 (2005)

    Article  MATH  Google Scholar 

  23. Wei, L. H., Tang, Z. M., Wang, R. Y., Yang, X. B.: Extensions of dominance-based rough set approach in incomplete information system. Autom. Control Comp. Sci. 42, 255–263 (2008)

    Article  Google Scholar 

  24. Yang, X. B., Xie, J., Song X. N., Yang, J. Y.: Credible rules in incomplete decision system based on descriptors. Knowl.-Based Syst. 22, 8–17 (2009)

    Article  Google Scholar 

  25. Luo G. Z., Yang, X. B.: Limited dominance-based rough set model and knowledge reductions in incomplete decision system. J. Inform. Sci. Eng. 26, 2199–2211 (2010)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang Jiangsu, 212003, P.R. China

    Xibei Yang

  2. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing Jiangsu, 210094, P.R. China

    Jingyu Yang

Authors
  1. Xibei Yang
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  2. Jingyu Yang
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© 2012 Science Press Beijing and Springer-Verlag Berlin Heidelberg

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Yang, X., Yang, J. (2012). Dominance-based Rough Sets in “*” Incomplete Information System. In: Incomplete Information System and Rough Set Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25935-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-25935-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25934-0

  • Online ISBN: 978-3-642-25935-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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