The Fuzzy Clustering Algorithm Based on AFS Topology
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.
KeywordsCluster Algorithm Fuzzy Cluster Fuzzy Concept Partition Tree Fuzzy Cluster Algorithm
Unable to display preview. Download preview PDF.
- 9.Bezdek, J.C.: Fuzzy Mathematics in pattern classification. Ph.D. dissertation. Dept. Appl. Math. Cornell Univ. Ithaca. NY (1973)Google Scholar
- 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.Liu, X.D., Zhang, Y.J.: The fuzzy theory based on AFS structure and AFS algebra. Dlian Maritime University Press, Dlian (1998)Google Scholar
- 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
- 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.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.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.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
- 21.Gao, X.B.: Fuzzy Clustering Analysis and its Applications. Xidian University Press, Xian (2004) (in chinese)Google Scholar