Asymmetric aggregation operator and its application to fuzzy clustering model

Computational Statistics and Data Analysis

Volumn 32, Issue 3-4, 2000, Pages 379-394

  Sato Ilic, Mika ^a   Sato, Yoshiharu ^b  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Additive clustering; Similarity data* t norm

Indexed keywords

FUZZY SETS; MATHEMATICAL MODELS;

ASYMMETRIC AGGREGATION OPERATORS; FUZZY CLUSTERING MODELS;

MATHEMATICAL OPERATORS;

EID: 0033900844     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(99)00091-2     Document Type: Article

References (24)

1. Bezdek, J.C., 1987. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York.
2. Clogg C.C. Latent structure models of mobility. Amer. J. Sociol. 86:1981;836-868.
3. Dave, R.N., Bhaswan, K., 1992. Adaptive fuzzy c-shells clustering and detection of ellipses, IEEE Trans. Neural Networks 3, 643-662.
4. Dunn J.C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybernet. 3:1973;32-57.
5. Fullér R. On Hamacher-sum of triangular fuzzy numbers. Fuzzy Sets and Systems. 42:1991;205-212.
6. Goodman L.A. Simple models for the analysis of association in cross-classifications having ordered categories. J. Amer. Statist. Assoc. 74:1979;537-552.
7. Gordon A.D. A review of hierarchical classification. J. Roy. Statist. Soc. Ser. A. 150:1987;119-137.
8. Hagenaars, J.A., 1990. Categorical Longitudinal Data. Sage Publications, Newbury Park, CA.
9. Hall, L.O., Bensaid, A.M. etal., 1992. A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain, IEEE Trans. Neural Networks 3, 672-682.
10. Harshman R.H., Green P.E., Wind Y., Lundy M.E. A model for the analysis of asymmetric data in marketing research. Marketing Sci. 1:1982;205-242.
11. Hubert L. Min and max hierarchical clustering using asymmetric similarity measures. Psychometrika. 38:1973;63-72.
12. Klir, G.J., Folger, T.A., 1988. Fuzzy Sets, Uncertainty, and Information. Prentice-Hall, Englewood Cliffs, NJ.
13. Menger K. Statistical metrics. Mathematics. 28:1942;535-537.
14. Ruspini E.H. A new approach to clustering. Inform. and Control. 15:1969;22-32.
15. Sato M., Sato Y. An additive fuzzy clustering model. Jpn. J. Fuzzy Theory Systems. 6:1994;185-204.
16. Sato, M., Sato, Y., 1995a. Extended fuzzy clustering models for asymmetric similarity. Fuzzy Logic and Soft Computing. World Scientific, Singapore, pp. 228-237.
17. Sato M., Sato Y. On a general fuzzy additive clustering model. Int. J. Intell. Automat. Soft Comput. 1(4):1995;439-448.
18. Schweizer, B., Sklar, A., 1983. Probabilistic Metric Space. North-Holland, New York.
19. Shepard R.N., Arabie P. Additive clustering: representation of similarities as combinations of discrete overlapping properties. Psychol. Rev. 86(2):1979;87-123.
20. Smith, M.H., 1992. Evaluation of performance and robustness of a parallel dynamic switching fuzzy system. Second International Workshop on Industrial Fuzzy Control and Intelligent Systems, pp. 163-172.
21. Takane, Y., Kiers, H.A.L., 1995. Latent class DEDICOM, Proceedings of 12th Symposium on Japan Classification Society, pp. 25-32.
22. Tarjan R.E. An improved algorithm for hierarchical clustering using strong components. Inform. Process. Lett. 17:1983;37-41.
23. Torgerson W.S. Multidimensional scaling: I. Theory and method. Psychometrika. 17:1952;401-419.
24. Zadeh L.A. Fuzzy sets. Inform. and Control. 8:1965;338-353.