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A discernibility matrix for the topological reduction

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Abstract

Discernibility matrices play an important role in the attribute reduction of information systems. The reduction of a family of general relations, which preserves the topological base, is an extension of the attribute reduction of information systems. In this paper, we construct a new discernibility matrix for the topological reduction of a family of general relations.

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References

  1. Guo G, Chen S, Chen L (2011) Soft subspace clustering with an improved feature weight self-adjustment mechanism. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0039-7

  2. Hall M, Holmes G (2003) Benchmarking attribute selection techniques for discrete class data mining. IEEE Trans Knowl Data Eng 15(6):1437–1447

    Article  Google Scholar 

  3. Hu Q, Pan W, An S, Ma P, Wei J (2010) An efficient gene selection technique for cancer recognition based on neighborhood mutual information. Int J Mach Learn Cybern 1(1–4):63–74

    Article  Google Scholar 

  4. Kondo M (2006) On the structure of generalized rough sets. Inf Sci 176:589–600

    Article  MathSciNet  MATH  Google Scholar 

  5. Lashin EF, Kozae AM, Abo Khadra AA, Medhat T (2005) Rough set theory for topological spaces. Int J Approx Reason 40:35–43

    Article  MathSciNet  MATH  Google Scholar 

  6. Lashin EF, Medhat T (2005) Topological reduction of information systems. Chaos Solitons Fractals 25:277–286

    Article  MATH  Google Scholar 

  7. Leung Y, Wu WZ, Zhang WX (2006) Knowledge acquisition in incomplete information systems: a rough set approach. Eur J Oper Res 168:164–180

    Article  MathSciNet  MATH  Google Scholar 

  8. Li J, Han G, Wen J, Gao X (2011) Robust tensor subspace learning for anomaly detection. Int J Mach Learn Cybern 2(2):89–98

    Article  Google Scholar 

  9. Mi JS, Wu WW, Zhang WX (2004) Approaches to knowledge reduction based on variable precision rough set model. Inf Sci 159:255–272

    Article  MathSciNet  MATH  Google Scholar 

  10. Nguyen HS, Slezak D (1999) Approximation reducts and association rules correspondence and complexity results. In: Zhong N, Skowron A, Oshuga S (eds) Proceedings of RSFDGrC99. Yamaguchi, Japan. LNAI, vol 1711, pp 137–145

  11. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 5:341–356

    Article  MathSciNet  Google Scholar 

  12. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston

  13. Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0034-z

  14. Poon B, Amin M A, Yan H (2011) Performance evaluation and comparison of PCA based human face recognition methods for distorted images. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0023-2

  15. Skowron A, Rauszer C (1992) 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 Academic Publishers, Boston, pp 331–362

  16. Slezak D (1998) Searching for dynamic reducts in inconsistent decision tables. In: Proceedings of IPMU98, Paris, France, vol 2, pp 1362–1369

  17. Wang XZ, Tsang E, Zhao SY, Chen DG, Yeung D (2007) Learning fuzzy rules from fuzzy examples based on rough set techniques. Inf Sci 177(20):4493–4514

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang XZ, Zhai JH, Lu SX (2008) Induction of multiple fuzzy decision trees based on rough set technique. Inf Sci 178(16):3188–3202

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang X Z, Li C G (2008) A definition of partial derivative of random functions and its application to RBFNN sensitivity analysis. Neurocomputing 71(7–9):1515–1526

    Article  Google Scholar 

  20. Wu WZ, Zhang WX, Li HZ (2003) Knowledge acquisition in incomplete fuzzy information systems via rough set approach. Expert Syst 20(5):280–286

    Article  Google Scholar 

  21. Wu W Z (2008) Attribute reduction based on evidence theory in incomplete decision systems. Inf Sci 178:1355–1371

    Article  Google Scholar 

  22. Wu WZ, Zhang M, Li HZ, Mi JS (2005) Knowledge reduction in random information systems via Dempster–Shafer theory of evidence. Inf Sci 174:143–164

    Article  MathSciNet  MATH  Google Scholar 

  23. Wiweger A (1989) On topological rough sets. Bull Pol Acad Sci 37(1–6):89–93

    MathSciNet  MATH  Google Scholar 

  24. Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259

    Article  MATH  Google Scholar 

  25. Zakowski W (1983) Approximation in the space \((U,\Uppi)\). Demonstr Math 16:761–769

    MathSciNet  MATH  Google Scholar 

  26. Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46:39–59

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Tsinghua University press, Beijing, pp 32–44

  28. Zhu W (2007) Topological approaches to covering generalized rough sets. Inf Sci 177:1499–1508

    Article  MATH  Google Scholar 

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Acknowledgments

The project is supported by the NNSF (Nos. 1067 1173, 10971186 and 71140004) of China, and the Foundations of Fujian Province in China (Nos. 2008F5066 and JA09165).

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Correspondence to Peirong Lin.

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Lin, P. A discernibility matrix for the topological reduction. Int. J. Mach. Learn. & Cyber. 3, 307–311 (2012). https://doi.org/10.1007/s13042-011-0064-6

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  • DOI: https://doi.org/10.1007/s13042-011-0064-6

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