Skip to main content

Three Granular Structure Models in Graphs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7414))

Abstract

The granular structures emphasize a multilevel and multiview understanding of problems. This paper gives a study on how to granulate a graph, and how to extract the granular structures in the graph. There are three kinds of objects in the graph, vertices, edges and the combinations of vertices and edges. Differing from previous researches on graph clustering which focused on the classification of vertices, we study three granular structure models for the three kinds of objects in the graph.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)

    Book  Google Scholar 

  2. Brandes, U., Gaertler, M., Wagner, D.: Experiments on Graph Clustering Algorithms. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 568–579. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Chen, G., Zhong, N., Yao, Y.Y.: Hypergraph Model of Granular Computing. In: 2008 IEEE International Conference on Granular Computing, pp. 80–85. IEEE Press, New York (2008)

    Google Scholar 

  4. Chen, G., Zhong, N.: Granular Structures in Graphs. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 649–658. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Flake, G.W., Tarjan, R.E., Tsioutsiouliklis, K.: Graph Clustering and Minimum Cut Trees. Internet Mathematics 1(1), 385–408 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hobbs, J.R.: Granularity. In: 9th International Joint Conference on Artificial Intelligence, pp. 432–435 (1985)

    Google Scholar 

  7. Luo, J., Yao, Y.: Granular State Space Search. In: Butz, C., Lingras, P. (eds.) Canadian AI 2011. LNCS (LNAI), vol. 6657, pp. 285–290. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Polkowski, L.: A Model of Granular Computing with Applications: Granules from Rough Inclusions in Information Systems. In: IEEE International Conference on Granular Computing, pp. 9–16 (2006)

    Google Scholar 

  10. Schaeffer, S.E.: Graph Clustering. Computer Science Review 1(1), 27–64 (2007)

    Article  MathSciNet  Google Scholar 

  11. Skowron, A., Stepaniuk, J.: Information Granules: Towards Foundations of Granular Computing. International Journal of Intelligent Systems 16, 57–85 (2001)

    Article  MATH  Google Scholar 

  12. Stell, A.J.: Granulation for Graphs. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 417–432. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Wong, S.K.M., Wu, D.: Automated Mining of Granular Database Scheme. In: IEEE International Conference on Fuzzy Systems, vol. 1, pp. 690–694 (2002)

    Google Scholar 

  14. 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 

  15. Yao, Y.Y.: The Art of Granular Computing. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 101–112. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Yao, Y., Miao, D., Zhang, N., Xu, F.: Set-Theoretic Models of Granular Structures. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS (LNAI), vol. 6401, pp. 94–101. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Yao, Y.Y., Zhong, N.: Granular Computing. Wiley Encyclopedia of Computer Science and Engineering 3, 1446–1453 (2009)

    Google Scholar 

  18. 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 

  19. Zhang, L., Zhang, B.: The Quotient Space Theory of Problem Solving. Fundamenta Informatcae 59, 287–298 (2004)

    MATH  Google Scholar 

  20. Zhu, W., Wang, F.Y.: On Three Types of Covering-based Rough Sets. IEEE Transactions on Knowledge and Data Engineering 19(8), 1131–1144 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, G., Zhong, N. (2012). Three Granular Structure Models in Graphs. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31900-6_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31899-3

  • Online ISBN: 978-3-642-31900-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics