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Tolerance Relation Based Granular Space

  • Conference paper
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3641))

Abstract

Granular computing as an enabling technology and as such it cuts across a broad spectrum of disciplines and becomes important to many areas of applications. In this paper, the notions of tolerance relation based information granular space are introduced and formalized mathematically. It is a uniform model to study problems in model recognition and machine learning. The key strength of the model is the capability of granulating knowledge in both consecutive and discrete attribute space based on tolerance relation. Such capability is reestablished in granulation and an application in information classification is illustrated. Simulation results show the model is effective and efficient.

This paper is supported by National Natural Science Foundation of China No. 60435010 and National Basic Research Priorities Programme No. 2003CB317004.

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References

  1. Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Dordrecht (2003)

    MATH  Google Scholar 

  2. Pal, S.K., Polkowski, L., Skowron, A.: Rough-Neural Computing: Techniques for Computing with Words. Springer Publishers, Heidelberg (2004)

    MATH  Google Scholar 

  3. Zhang, B., Zhang, L.: Theory and Application of Problem Solving. Elsevier Science Publishers, North-Holland (1992)

    Google Scholar 

  4. Zadeh, L.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 19, 111–127 (1997)

    Article  MathSciNet  Google Scholar 

  5. Pawlak, Z.: Rough Sets Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  6. Yao, Y.Y., Zhong, N.: Granular Computing Using Information Table. In: Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.) Data Miming, Rough Sets and Granular Computing, pp. 102–124. Physica, Heidelberg (2000)

    Google Scholar 

  7. Hu, X.H., Cercone, N.: Learning in relational database: a rough set approach. Computational Intelligence 11(2), 323–338 (1995)

    Article  Google Scholar 

  8. Wang, G.Y.: Rough set theory and knowledge acquisition. XI’an Jiaotong University Press, Xi’an (2001)

    Google Scholar 

  9. Mollestad, T., Skowron, A.: A rough set framework for data mining of propositional default rules. In: Foundations of Intelligent Systems of the 9th International Symposium, pp. 448–457. Springer, Heidelberg (1996)

    Google Scholar 

  10. Wang, G.Y., He, X.: A Self-Learning Model under Uncertain Condition. Chinese Journal of SoftWare 14(6), 1096–1102 (2003)

    MATH  Google Scholar 

  11. Yao, Y.Y.: A partition model of granular computing. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Yao, Y.Y.: Granular computing. In: The 4th Chinese National Conference on Rough Sets and Soft Computing, pp. 4–10 (2004)

    Google Scholar 

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

    Google Scholar 

  14. Marcus, S.: Tolerance Rough Sets, Cech Topologies, Learning Processes. Bulletin of the Polish Academy of Sciences, Technical Sciences 42(3), 471–487 (1994)

    MATH  Google Scholar 

  15. Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253 (1996)

    MATH  MathSciNet  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, 100080, Beijing, China

    Zheng Zheng, Hong Hu & Zhongzhi Shi

  2. Graduate School of the Chinese Academy of Sciences, 100039, Beijing, China

    Zheng Zheng

Authors
  1. Zheng Zheng
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  2. Hong Hu
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  3. Zhongzhi Shi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2 Canada, Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, P.O. Box, Poland

    Dominik Ślęzak

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Guoyin Wang

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

    Marcin Szczuka

  4. Department of Computer Science, Brock University, St. Catharines, L2S 3A1, Ontario, Canada

    Ivo Düntsch

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

    Yiyu Yao

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© 2005 Springer-Verlag Berlin Heidelberg

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Zheng, Z., Hu, H., Shi, Z. (2005). Tolerance Relation Based Granular Space. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_70

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  • DOI: https://doi.org/10.1007/11548669_70

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28653-0

  • Online ISBN: 978-3-540-31825-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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