Inconsistent Dominance Principle Based Attribute Reduction in Ordered Information Systems

  • Guang-Lei Gou
  • Guoyin WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9436)


Dominance-based rough set is an important model for ordered decision system, in which knowledge reduction is one of the most important problems. The preference ordering of decision between objects is ignored in existed reduction. This paper proposed a knowledge reduction approach based on inconsistent dominance principle, with which two objects are discernable. Furthermore, the judgment theorems and the discernable matrix are investigated, from which we can obtain a new approach to knowledge reduction in ordered decision system.


Ordered decision system Knowledge reduction Inconsistent dominance principle 



This work is supported by the National Science and Technology Major Project (2014ZX07104-006) and the Hundred Talents Program of CAS (NO.Y21Z110A10).


  1. 1.
    Dembczyński, K., Greco, S., Kotłowski, W., Słowiński, R.: Quality of Rough Approximation in Multi-criteria Classification Problems. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 318–327. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  2. 2.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough Approximation by Dominance Relations. Int. J. Intell. Syst. 17(2), 153–171 (2002)CrossRefGoogle Scholar
  3. 3.
    Thangavel, K., Pethalakshmi, A.: Dimensionality reduction based on rough set theory: a review. Appl. Soft Comput. 9(1), 1–12 (2009)CrossRefGoogle Scholar
  4. 4.
    Zhang, W.X., Mi, J.S., Wu, W.Z.: Approaches to knowledge reductions in inconsistent systems. Int. J. Intell. Syst. 18(9), 989–1000 (2003)CrossRefGoogle Scholar
  5. 5.
    Miao, D.Q., Zhao, Y., Yao, Y.Y., Li, H.X., Xu, F.F.: Relative reducts in consistent and inconsistent decision tables of the Pawlak rough set model. Inf. Sci. 179(24), 4140–4150 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Qian, Y., Liang, J., Pedrycz, W., Dang, C.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artif. Intell. 174(9), 597–618 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough approximation of a preference relation by dominance relations. Eur. J. Oper. Res. 117(98), 63–83 (1999)CrossRefGoogle Scholar
  8. 8.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)CrossRefGoogle Scholar
  9. 9.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur. J. Oper. Res. 138(2), 247–259 (2002)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Xu, W.H., Zhang, W.X.: Knowledge reductions in inconsistent information systems based on dominance relations. Comput. Sci. 33(2), 182–184 (2006) (in Chinese)Google Scholar
  11. 11.
    Xu, W.H., Zhang W.X.: Matrix computation for assignment reduction in information systems based on dominance relations. Comput. Eng. 33(14), 4–7 (2007) (in Chinese)Google Scholar
  12. 12.
    Xu, W.H., Zhang, W.X.: Methods for knowledge reduction in inconsistent ordered information systems. J. Appl. Math. Comput. 26(1), 313–323 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Xu, W.H., Li, Y., Liao, X.: Approaches to attribute reductions based on rough set and matrix computation in inconsistent ordered information systems. Knowl. Based Syst. 27(3), 78–91 (2012)CrossRefGoogle Scholar
  14. 14.
    Chen, J., Wang, G.Y., Hu, J.: Positive domain reduction based on dominance relation in inconsistent system. Comput. Sci. 35(3), 216–218, 227 (2008) (in Chinese)Google Scholar
  15. 15.
    Inuiguchi, M., Yoshioka, Y.: Several reducts in dominance-based rough set approach. In: Huynh, V.N., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds.) Interval/Probabilistic Uncertainty and Non-Classical Logics. ASC, vol. 46, pp. 163–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Kusunoki, Y., Inuiguchi, M.: A unified approach to reducts in dominance-based rough set approach. Soft Comput. 14(5), 507–515 (2010)CrossRefGoogle Scholar
  17. 17.
    Susmaga, R.: Reducts and constructs in classic and dominance-based rough sets approach. Inf. Sci. 271(7), 45–64 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dembczyński, K., Greco, S., Słowiński, R.: Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur. J. Oper. Res. 198(2), 626–636 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (, which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Authors and Affiliations

  1. 1.School of Information Science and TechnologySouthwest Jiaotong UniversityChengduChina
  2. 2.Big Data Mining and Applications CenterChongqing Institute of Green and Intelligent Technology, CASChongqingChina
  3. 3.School of Computer Science and EngineeringChongqing University of TechnologyChongqingChina

Personalised recommendations