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Three-Way Weighted Entropies and Three-Way Attribute Reduction

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Rough Sets and Knowledge Technology (RSKT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8818))

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Abstract

Rough set theory (RS-Theory) is a fundamental model of granular computing (GrC) for uncertainty information processing, and information entropy theory provides an effective approach for its uncertainty representation and attribute reduction. Thus, this paper hierarchically constructs three-way weighted entropies (i.e., the likelihood, prior, and posterior weighted entropies) by adopting a GrC strategy from the concept level to classification level, and it further explores three-way attribute reduction (i.e., the likelihood, prior, and posterior attribute reduction) by resorting to a novel approach of Bayesian inference. From two new perspectives of GrC and Bayesian inference, this study provides some new insights into the uncertainty measurement and attribute reduction of information theory-based RS-Theory.

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References

  1. Pawlak, Z.: Rough sets. International Journal of Information and Computer Science 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  2. Shannon, C.E.: The mathematical theory of communication. The Bell System Technical Journal 27(3–4), 373–423 (1948)

    MathSciNet  Google Scholar 

  3. Miao, D.Q.: Rough set theory and its application in machine learning (Ph. D. Thesis). Beijing, Institute of Automation, The Chinese Academy of Sciences (1997)

    Google Scholar 

  4. Beaubouef, T., Petry, F.E., Arora, G.: Information-theoretic measures of uncertainty for rough sets and rough relational databases. Information Sciences 109(1-4), 185–195 (1998)

    Article  Google Scholar 

  5. Slezak, D.: Approximate entropy reducts. Fundamenta Informaticae 53, 365–390 (2002)

    MathSciNet  Google Scholar 

  6. Miao, D.Q., Hu, G.R.: A heuristic algorithm for reduction of knowledge. Chinese Journal of Computer Research & Development 36, 681–684 (1999)

    Google Scholar 

  7. Miao, D.Q., Wang, J.: An information representation of the concepts and operations in rough set theory. Journal of Software 10(2), 113–116 (1999)

    Google Scholar 

  8. Liang, J.Y., Qian, Y.H., Chu, D.Y., Li, D.Y., Wang, J.H.: The algorithm on knowledge reduction in incomplete information systems. Fuzziness and Knowledge-Based Systems 10, 95–103 (2002)

    Article  MATH  Google Scholar 

  9. Liang, J., Shi, Z., Li, D., Wierman, M.: Information entropy, rough entropy and knowledge granularity in incomplete information systems. International Journal of General Systems 35(6), 641–654 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, G.Y., Yu, H., Yang, D.C.: Decision table reduction based on conditional information entropy. Chinese Journal of Computers 25, 759–766 (2002)

    MathSciNet  Google Scholar 

  11. Wang, G.Y., Zhao, J., An, J.J., Wu, Y.: A comparative study of algebra viewpoint and information viewpoint in attribute reduction. Fundamenta Informaticae 68(3), 289–301 (2005)

    MathSciNet  MATH  Google Scholar 

  12. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2006)

    Google Scholar 

  13. Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 111–127 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lin, T.Y.: Granular computing: from rough sets and neighborhood systems to information granulation and computing with words. In: European Congress on Intelligent Techniques and Soft Computing, pp. 1602–1606 (1997)

    Google Scholar 

  15. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 1–17. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. Miao, D.Q., Zhang, X.Y.: Change uncertainty of three-way regions in knowledge-granulation. In: Liu, D., Li, T.R., Miao, D.Q., Wang, G.Y., Liang, J.Y. (eds.) Three-Way Decisions and Granular Computing, pp. 116–144. Science Press, Beijing (2013)

    Google Scholar 

  18. Zhang, X.Y., Miao, D.Q.: Quantitative information architecture, granular computing and rough set models in the double-quantitative approximation space on precision and grade. Information Sciences 268, 147–168 (2014)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, P.R. China

    Xianyong Zhang & Duoqian Miao

  2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610068, P.R. China

    Xianyong Zhang

Authors
  1. Xianyong Zhang
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  2. Duoqian Miao
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Corresponding author

Correspondence to Xianyong Zhang .

Editor information

Editors and Affiliations

  1. Tongji University, Shanghai, China

    Duoqian Miao

  2. Department of Electrical and Computer En, University of Alberta, Edmonton, Alberta, Canada

    Witold Pedrycz

  3. University of Warsaw, Warsaw, Poland

    Dominik Ślȩzak

  4. University of Applied Sciences, München, Germany

    Georg Peters

  5. Tianjin University, Tianjin, China

    Qinghua Hu

  6. Tongji University, Shanghai, China

    Ruizhi Wang

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© 2014 Springer International Publishing Switzerland

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Zhang, X., Miao, D. (2014). Three-Way Weighted Entropies and Three-Way Attribute Reduction. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds) Rough Sets and Knowledge Technology. RSKT 2014. Lecture Notes in Computer Science(), vol 8818. Springer, Cham. https://doi.org/10.1007/978-3-319-11740-9_65

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  • DOI: https://doi.org/10.1007/978-3-319-11740-9_65

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11739-3

  • Online ISBN: 978-3-319-11740-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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