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The Attribute Reductions Based on Indiscernibility and Discernibility Relations

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

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Abstract

Knowledge reduction and knowledge discovery in information systems are important topics of rough set theory. Based on the relative indiscernibility relation and relative discernibility relation of decision systems, the notions of \(\lambda \) reduction and \(\mu \) reduction are proposed. The judgement theorems for \(\lambda \) consistent set and \(\mu \) consistent set are provided. The discernibility matrices with respect to \(\lambda \) reduction and \(\mu \) reduction are obtained and the reduction approaches are presented. Furthermore, the relationships among \(\lambda \) reduction, \(\mu \) reduction, positive region reduction and assignment reduction are analyzed.

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References

  1. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)

    Article  Google Scholar 

  2. Thangavela, K., Pethalakshmi, A.: Dimensionality reduction based on rough set theory: a review. Appl. Soft Comput. 9, 1–12 (2009)

    Article  Google Scholar 

  3. Krawczak, M., Szkatula, G.: An approach to dimensionality reduction in time series. Inf. Sci. 260, 15–36 (2014)

    Article  MathSciNet  Google Scholar 

  4. Pawlak, Z.: Rough set approach to knowledge-based decision support. Eur. J. Oper. Res. 99, 48–57 (1997)

    Article  Google Scholar 

  5. Kryszkiewicz, M.: Comparative studies of alternative type of knowledge reduction in inconsistent systems. Int. J. Intell. Syst. 16(1), 105–120 (2001)

    Article  Google Scholar 

  6. Kryszkiewicz, M.: Certain, generalized decision, and membership distribution reducts versus functional dependencies in incomplete systems. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 162–174. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73451-2_18

    Chapter  Google Scholar 

  7. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178(17), 3356–3372 (2008)

    Article  MathSciNet  Google Scholar 

  8. Zhang, W.X., Mi, J.S., Wu, W.Z.: Knowledge reduction in inconsistent information systems. Chin. J. Comput. 26, 12–18 (2003)

    MathSciNet  Google Scholar 

  9. Zhang, W.X., Mi, J.S., Wu, W.Z.: Approaches to knowledge reductions in inconsistent systems. Int. J. Intell. Syst. 18, 989–1000 (2003)

    Article  Google Scholar 

  10. 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, 4140–4150 (2009)

    Article  MathSciNet  Google Scholar 

  11. Meng, Z.Q., Shi, Z.Z.: Extended rough set-based attribute reduction in inconsistent incomplete decision systems. Inf. Sci. 204, 44–66 (2012)

    Article  MathSciNet  Google Scholar 

  12. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory. Kluwer, Dordrecht (1992)

    Google Scholar 

  13. Chen, D., Wang, C., Hu, Q.: A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf. Sci. 177(17), 3500–3518 (2007)

    Article  MathSciNet  Google Scholar 

  14. Qian, Y.H., Liang, J.Y., Li, D.Y., Wang, F., Ma, N.: Approximation reduction in inconsistent incomplete decision tables. Knowl.-Based Syst. 23(5), 427–433 (2010)

    Article  Google Scholar 

  15. Li, M., Shang, C.X., Feng, S.Z., Fan, J.P.: Quick attribute reduction in inconsistent decision tables. Inf. Sci. 254, 155–180 (2014)

    Article  MathSciNet  Google Scholar 

  16. Meng, Z.Q., Shi, Z.Z.: A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets. Inf. Sci. 179, 2774–2793 (2009)

    Article  MathSciNet  Google Scholar 

  17. Shen, Q., Chouchoulas, A.: A modular approach to generating fuzzy rules with reduced attributes for the monitoring of complex systems. Eng. Appl. Artif. Intell. 13(3), 263–278 (2000)

    Article  Google Scholar 

  18. Wang, G.Y., Yu, H., Yang, D.: Decision table reduction based on conditional information entropy. Chin. J. Comput. 25(7), 759–766 (2002)

    MathSciNet  Google Scholar 

  19. Orłowska, E.: Introduction: what you always wanted to know about rough sets. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, vol. 13, pp. 1–20. Physica Verlag, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Orłowska, E.: Logic of nondeterministic information. Stud. Log. 44(1), 91–100 (1985)

    Article  MathSciNet  Google Scholar 

  21. Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundam. Inform. 15(1), 61–79 (1991)

    MathSciNet  MATH  Google Scholar 

  22. Zhao, Y., Yao, Y.Y., Luo, F.: Data analysis based on discernibility and indiscernibility. Inf. Sci. 177(22), 4959–4976 (2007)

    Article  Google Scholar 

  23. Qin, K., Jing, S.H.: The attribute reduction of decision systems based on indiscernibility and discernibility. J. Comput. Sci. (submitted)

    Google Scholar 

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Acknowledgments

The authors are highly grateful to the anonymous referees for their insightful comments and valuable suggestions which greatly improve the quality of this paper. This work has been partially supported by the National Natural Science Foundation of China (Grant Nos. 61473239, 61372187), and the open research fund of key laboratory of intelligent network information processing, Xihua University (szjj2014-052).

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Authors and Affiliations

  1. College of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Keyun Qin & Sihui Jing

Authors
  1. Keyun Qin
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  2. Sihui Jing
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Correspondence to Keyun Qin .

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Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, SK, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Qin, K., Jing, S. (2017). The Attribute Reductions Based on Indiscernibility and Discernibility Relations. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-60837-2_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

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