The Fuzzy Clustering Algorithm Based on AFS Topology

  • Rui Ding
  • Xiaodong Liu
  • Yan Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


This paper establishes a new metric space for the clustering problems. The neighbors on the object set induced by the topology molecular lattice on  ∗  EI algebra are given and a new distance based on the neighbors is proposed. In the proposed clustering algorithm, the Euclidean metric is replaced by the new distance based on the order relationship of the samples on the attributes. As a result, using the method to Iris data we show it has a better result and clearer classification than the other clustering algorithm based on the Euclidean metric. This study shows that the AFS topology fuzzy clustering algorithm can obtain an high clustering accuracy according to order relationship.


Cluster Algorithm Fuzzy Cluster Fuzzy Concept Partition Tree Fuzzy Cluster Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 18, 338–353 (1965)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Liu, X.D.: The fuzzy theory based on AFS algebras and AFS structure. J. Math. Anal. Appl. 217, 459–478 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Liu, X.D.: The fuzzy sets and systems based on AFS structure, EI algebra and EII algebra. Fuzzy Sets Syst. 95, 179–188 (1998)MATHCrossRefGoogle Scholar
  4. 4.
    Liu, X.D.: A new mathematical axiomatic system of fuzzy sets and systems. J. Fuzzy Math. 3, 559–560 (1995)MATHMathSciNetGoogle Scholar
  5. 5.
    Liu, X.D.: Two algebra structures of AFS structure. J. Fuzzy Math. 3, 561–562 (1995)MATHMathSciNetGoogle Scholar
  6. 6.
    Liu, X.D.: The topology on AFS algebra and AFS structure. J. Math. Anal. Appl. 217, 479–489 (1998)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Wang, G.j.: Theory of topological molecular lattices. Fuzzy Sets Syst. 47, 351–376 (1992)MATHCrossRefGoogle Scholar
  8. 8.
    Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybern. 3(3), 32–57 (1974)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bezdek, J.C.: Fuzzy Mathematics in pattern classification. Ph.D. dissertation. Dept. Appl. Math. Cornell Univ. Ithaca. NY (1973)Google Scholar
  10. 10.
    Keller., J.M., Gray, M.R., Givens Jr., J.A.: A fuzzy K-nearest neighbors algorithm. IEEE Trans. Syst. Man, Cybern. SMC-15(4), 580–585 (1985)Google Scholar
  11. 11.
    Liu, X.D., Zhang, Y.J.: The fuzzy theory based on AFS structure and AFS algebra. Dlian Maritime University Press, Dlian (1998)Google Scholar
  12. 12.
    Liu, X.D., Chai, T.Y., Wang, W.: AFS Fuzzy Logic Systems and Its Applications to Model and Control. International Journal of Information and Systems Sciences 2(3), 1–21 (2006)MathSciNetGoogle Scholar
  13. 13.
    Liu, X.D., Chai, T.Y., Wang, W.: Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I, II. Information Sciences. Revised (2005)Google Scholar
  14. 14.
    Liu, X.D., Wang, W., Chai, T.Y.: The Fuzzy Clustering Analysis Based on AFS Theory. IEEE Trans. Syst. Man, Cybern.- part B: Cybernetics 35(3), 1013–1027 (2005)CrossRefGoogle Scholar
  15. 15.
    Liu, X.D., Zhu, K.J., Huang, H.Z.: The representations of fuzzy concepts based on the fuzzy matrix theory and the AFS theory. In: Proc. IEEE Int. Symp. Intelligent Control, Houston, TX, October 2003, pp. 1006–1011 (2003)Google Scholar
  16. 16.
    Liu, X.D., Witold, P., Zhang, Q.L.: Axiomatics fuzzy sets logic. In: Proc. IEEE Int. Conf. Fuzzy Systems, St. Louis, MO, vol. 1, pp. 55–60 (2003)Google Scholar
  17. 17.
    Liu, X.D., Witold, P.: The Development of Fuzzy Decision Trees in the Framework of Axiomatic Fuzzy Set Logic. Applied Soft Computing, available online (accepted, 2005)Google Scholar
  18. 18.
    Liu, X.D., Zhang, L.S., Zhu, K.J., Zhang, Q.L.: The Structures of EI Algebras Generated by Information Attributes. Int. J. Intelligent Systems Technologies and Applications (in press)Google Scholar
  19. 19.
    Liu, X.D., Liu, W.Q.: Credit Rating Analysis with AFS Fuzzy Logic. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 1198–1204. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Graver, J.E., Watkins, M.E.: Combinatorics with Emphasis on the Theory of Graphs. Springer, New York (1977)MATHGoogle Scholar
  21. 21.
    Gao, X.B.: Fuzzy Clustering Analysis and its Applications. Xidian University Press, Xian (2004) (in chinese)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rui Ding
    • 1
  • Xiaodong Liu
    • 1
    • 2
  • Yan Chen
    • 1
  1. 1.Economics and Management CollegeDalian Maritime UniversityDalianP.R. China
  2. 2.Research Center of Information and ControlDalian University of TechnologyDalianP.R. China

Personalised recommendations