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The Information Entropy of Rough Relational Databases

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2639))

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Abstract

Beaubouef, Petry and Buckles proposed the generalized rough set database analysis (GRSDA) to discuss rough relational databases. Given any rough relational database (U, A) and an attribute a ∈ A, as in rough set theory, a definition of the lower and upper approximations based on φ, a is given. The entropy and conditional entropy of similarity relations in a rough relational database are defined. The examples show that the entropy of a similarity relation does not decrease as the similarity relation is refined. It will be proved that given any two similarity relations φ and ψ, defined by a set C of conditional attributes and a decision attribute d, respectively, if d similarly depends on C in a rough relational database then the conditional entropy of φ with respect to ψ is equal to the entropy of φ.

The project was partially supported by the National NSF of China and the National 973 Project of China under the grant number G1999032701. The first author was partially supported by the National Laboratory of Software Development Environment. The second auther was partially supported by the Yunnan Provincial NSF grant 2000F0049M and 2001F0006Z.

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References

  1. Beaubouef, T., Petry, F. E. and Buckles, B. P., Extension of the relational database and its algebra with rough set techniques, Computational Intelligence 11(1995), 1233–245.

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Düntsch, I. and Gediga, G., Uncertainty measures of rough set prediction, Artificial Intelligence 106(1998), 109–137.

    Article  MATH  MathSciNet  Google Scholar 

  4. Pawlak, Z., Rough sets — theoretical aspects of reasoning about data, Kluwer Academic Publishers, 1991.

    Google Scholar 

  5. Polkowski, L., Skowron, A. and Zytkow, J., Tolerance based rough sets, in: T. Y. Lin and A. M. Wildberger (eds.), Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Simulation Councils, Inc., San Diego, 1995, 55–58.

    Google Scholar 

  6. Skowron, A. and Stepaniuk, J., Tolerance approximation spaces, Fundamenta Informaticae 27(1996), 245–253.

    MATH  MathSciNet  Google Scholar 

  7. Yao, Y. Y., Wong, S. K. M. and Lin, T. Y., A review of rough set models, in: T. Y. Lin, N. Cercone (eds.), Roght sets and data mining: analysis for imprecise data, Kluwer Academic Pub., Boston, London, Dordrecht, 1997, 47–75.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Yuefei Sui

  2. Department of Computer Science, Yunnan Normal University, Kunming, China

    Youming Xia

  3. Institute of Software, Chinese Academy of Sciences, Beijing, China

    Ju Wang

Authors
  1. Yuefei Sui
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  2. Youming Xia
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  3. Ju Wang
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Editor information

Editors and Affiliations

  1. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, P.R. China

    Guoyin Wang

  2. Department of Computer Science, Nanchang University, Nanchang, 330029, P.R. China

    Qing Liu

  3. Department of Computer Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Yiyu Yao

  4. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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© 2003 Springer-Verlag Berlin Heidelberg

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Sui, Y., Xia, Y., Wang, J. (2003). The Information Entropy of Rough Relational Databases. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_48

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  • DOI: https://doi.org/10.1007/3-540-39205-X_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14040-5

  • Online ISBN: 978-3-540-39205-7

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