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Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions

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Foundations of Intelligent Systems (ISMIS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2871))

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Abstract

A model of granular computing (GrC) is proposed by reformulating, re-interpreting, and combining results from rough sets, quotient space theory, and belief functions. Two operations, called zooming-in and zooming-out operations, are used to study connections between the elements of a universe and the elements of a granulated universe, as well as connections between computations in the two universes. The operations are studied with respect to multi-level granulation structures.

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References

  1. Brink, C.: Power structures. Algebra Universalis 30, 177–216 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bryniarski, E.: A calculus of rough sets of the first order. Bulletin of the Polish Academy of Sciences, Mathematics 37, 71–77 (1989)

    MATH  MathSciNet  Google Scholar 

  3. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  4. Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.): Rough Set Theory and Granular Computing. Springer, Berlin (2003)

    MATH  Google Scholar 

  5. Jardine, N., Sibson, R.: Mathematical Taxonomy. Wiley, New York (1971)

    MATH  Google Scholar 

  6. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  7. Lin, T.Y.: Topological and fuzzy rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer Academic Publishers, Boston (1992)

    Google Scholar 

  8. Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.): Rough Sets, Granular Computing and Data Mining. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  11. Serra, J.: Imagine Analysis and Mathematical Morphology. Academic Press, London (1982)

    Google Scholar 

  12. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  13. Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15, 291–317 (1996)

    Article  MATH  Google Scholar 

  14. Yao, Y.Y.: On generalizing Pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 298–307. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Yao, Y.Y.: Granular computing: basic issues and possible solutions. In: Proceedings of the 5th Joint Conference on Information Sciences, pp. 186–189 (2000)

    Google Scholar 

  16. Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent Systems 16, 87–104 (2001)

    Article  MATH  Google Scholar 

  17. Yao, Y.Y., Noroozi, N.: A unified framework for set-based computations. In: Proceedings of the 3rd International Workshop on Rough Sets and Soft Computing, The Society for Computer Simulation, pp. 252–255 (1995)

    Google Scholar 

  18. Yao, Y.Y., Wong, S.K.M.: Representation, propagation and combination of uncertain information. International Journal of General Systems 23, 59–83 (1994)

    Article  MATH  Google Scholar 

  19. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 47–75. Kluwer Academic Publishers, Boston (1997)

    Google Scholar 

  20. Zadeh, L.A.: 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 

  21. Zhang, B., Zhang, L.: Theory and Applications of Problem Solving. North- Holland, Amsterdam (1992)

    MATH  Google Scholar 

  22. Zhang, L., Zhang, B.: The quotient space theory of problem solving. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 11–15. Springer, Heidelberg (2003)

    Google Scholar 

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Author information

Authors and Affiliations

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

    Yiyu (Y. Y. ) Yao

  2. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Churn-Jung Liau

  3. Department of Information Engineering, Maebashi Institute of Technology, Maebashi, 371, Japan

    Ning Zhong

Authors
  1. Yiyu (Y. Y. ) Yao
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  2. Churn-Jung Liau
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  3. Ning Zhong
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Editor information

Editors and Affiliations

  1. The International WIC Institute, Beijing University of Technology, China

    Ning Zhong

  2. Department of Computer Science, University of North Carolina, NC 28223, Charlotte, USA

    Zbigniew W. Raś

  3. Shimane University, 89-1 Enya-cho Izumo, 6938501, Shimane, Japan

    Shusaku Tsumoto

  4. Department of Informatics, Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi, 819-0395, Fukuoka, Japan

    Einoshin Suzuki

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© 2003 Springer-Verlag Berlin Heidelberg

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Yao, Y.(.Y.)., Liau, CJ., Zhong, N. (2003). Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds) Foundations of Intelligent Systems. ISMIS 2003. Lecture Notes in Computer Science(), vol 2871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39592-8_21

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  • DOI: https://doi.org/10.1007/978-3-540-39592-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20256-1

  • Online ISBN: 978-3-540-39592-8

  • eBook Packages: Springer Book Archive

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