Three-way fuzzy clustering models for LR fuzzy time trajectories

Computational Statistics and Data Analysis

Volumn 43, Issue 2, 2003, Pages 149-177

  Coppi, Renato ^a   D'Urso, Pierpaolo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Cross sectional and or longitudinal studies; Dynamic fuzzy clustering; LR fuzzy time arrays; LR fuzzy time trajectories; Web advertising

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS;

FUZZY CLUSTERING;

FUZZY SETS;

FUZZY MATHEMATICS;

EID: 0038006805     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(02)00226-8     Document Type: Article

References (58)

1. Bezdek J.C. Numerical taxonomy with fuzzy sets J. Math. Biol. 1 1974 57 71
2. Bezdek J.C. A convergence theorem for fuzzy ISODATA clustering algorithms IEEE Trans. Pattern Anal. Mach. Intell. 2 1980 1 8
3. Bezdek J.C. Pattern Recognition with Fuzzy Objective Function Algorithms 1981 Plenum Press New York
4. Bezdek J.C. Hathaway R.J. Sabin M.J. Tncker W.T. Convergence theory for fuzzy c-means: counterexamples and repairs Trans. Systems, Man Cybernet. 17 1987 873 877
5. Bloch I. On fuzzy distances and their use in image processing under imprecision Pattern Recognition 32 1999 1873 1895
6. ∞ norms IEEE Trans. Systems, Man, Cybernet. 21 1991 545 554
7. Chen S.M. Yeh M.S. Hsio P.Y. A comparison of similarity measures of fuzzy values Fuzzy Sets and Systems 72 1995 79 89
8. Coppi R. D'Urso P. Fuzzy time arrays and dissimilarity measures for fuzzy time trajectories Kiers H.A.L. Rasson J.P. Groenen P.J.F. Schader M. Data Analysis, Classification, and Related Methods 2000 273 278 Springer Heidelberg
9. Coppi, R., D'Urso, P., 2002. Fuzzy k-means clustering models for triangular fuzzy time trajectories. Statist. Methods Appl. 11 (1), 21-40.
10. De Luca A. Termini S. A definition of non-probabilistic entropy in the setting of fuzzy set theory Inform. Control 20 1972 301 312
11. Diamond P. Fuzzy least squares Inform. Sci. 46 1988 141 157
12. Diamond P. Kloeden P. Metrics Spaces of Fuzzy Sets, Theory and Applications 1994 World Scientific Singapore
13. Dubois, D., Prade, H., 1983. On distance between fuzzy points and their use for plausible reasoning. Internat. Conf. Systems, Man Cybernet., 300-303.
14. Dubois D. Prade H. Possibility Theory 1988 Plenum Press New York
15. Dunn J.C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters J. Cybernet. 3 1974 32 57
16. D'Urso, P., 2001. Fuzzy C-means clustering models for time data arrays, submitted.
17. El-Sonbaty Y. Ismail M.A. Fuzzy clustering for symbolic data IEEE Trans. Fuzzy Systems 6 2 1998 195 204
18. Everitt B.S. Landau S. Leese M. Clustering Analysis 2001 Arnold London
19. Goetshel R. Voxman W. Topological properties of fuzzy numbers Fuzzy Sets Systems 10 1983 87 99
20. Harshman R.A. Lundy M.E. Data preprocessing and the extended PARAFAC model Law H.G. Snyder C.W. Hattie J.A. McDonald R.P. Research Methods for Multimode Data Analysis 1984 216 284 Praeger New York
21. Hathaway R.J. Bezdek J.C. Recent convergence results for the fuzzy c-means clustering algorithms J. Classification 5 1988 237 247
22. Hathaway R.J. Davenport J.W. Bezdek J.C. Relational duals of the c-means clustering algorithms Pattern Recognition 22 1989 205 212
23. Heiser W.J. Groenen P.J.F. Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima Psychometrika 62 1997 63 83
24. Ichino M. Yaguchi H. Generalized Minkowsky metrics for mixed feature-type data analysis IEEE Trans. Systems, Man Cybernet. 24 4 1994 698 708
25. Jajuga K. L1-norm based fuzzy clustering Fuzzy Sets and Systems 39 1991 43 50
26. Kaufman A. Introduction to the Theory of Fuzzy Subsets: Fundamental Theoretical Elements 1973 Academic Press New York
27. Kiers H.A.L. Towards a standardized notation and terminology in multiway analysis J. Chemometrics 14 2000 105 122
28. Koa ̌melj K. A two-step procedure for clustering time varying data J. Math. Sociol. 12 3 1986 315 326
29. Koašmelj K. Batagelj V. Cross-sectional approach for clustering time varying data J. Classification 7 1990 99 109
30. Liang G.S. Wang M.J.J. A fuzzy multi-criteria decision-making method for facility site selection Internat. J. Prod. Res. 29 1991 2313 2330
31. Liou T.S. Wang M.J.J. Subjective assessment of mental workload-a fuzzy linguistic multicriteria approach Fuzzy Sets and Systems 62 1994 155 165
32. Lowen R. Peeters W. Distances between fuzzy sets representing grey level images Fuzzy Sets and Systems 99 1998 135 150
33. 1 fuzzy c-means and its termination. Research Report ISE-TR-95-127, University of Tsukuba.
34. Miyamoto S. Umayahara K. Two methods of fuzzy c-means and classification functions Rizzi A. Vichi M. Bock H.H. Advances in Data Science and Classification 1998 105 110 Springer Berlin
35. Näther W. On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data Metrika 51 2000 201 221
36. Pappis C.P. Karacapilidis N.I. A comparative assessment of measures of similarity of fuzzy values Fuzzy Sets and Systems 56 1993 171 174
37. Raj P.A. Kumar D.N. Ranking alternatives with fuzzy weights using maximizing set and minimizing set Fuzzy Sets and Systems 105 1999 365 375
38. Ravi T.V. Gowda K.C. An ISODATA clustering procedure for symbolic objects using a distributed genetic algorithm Pattern Recognition Lett. 20 1999 659 666
39. Rosenfeld A. Fuzzy digital topology Inform. Control 40 1979 76 87
40. Roubens M. Pattern classification problems and fuzzy sets Fuzzy Sets and Systems 1 1978 239 253
41. Rousseeuw P.J. Trauwaert E. Kaufman L. Fuzzy clustering with high contrast J. Comput. Appl. Math. 64 1995 81 90
42. Rousseeuw P.J. Kaufman L. Trauwaert E. Fuzzy clustering using scatter matrices Comput. Statist. Data Anal. 23 1996 135 151
43. Ruspini, E.H., Bonissone, P., Pedrycz, W. (Eds.) 1998. Handbook of Fuzzy Computation. Institute of Physics Publishing, Bristol, Philadelphia.
44. Saporta, G., Lavallard, F., 1996. L'Analyse des Données Évolutives. Méthodes et Applications. Éditions Technip, Paris.
45. Sato M. Sato Y. On a multicriteria fuzzy clustering method for 3-way data Internat. J. Uncertainty, Fuzziness Knowledge-Based Systems 2 1994 127 142
46. Sato, M., Sato, Y., 1995. Fuzzy clustering model for fuzzy data. Proc. IEEE International Conference on Fuzzy Systems, 4, 2123-2128.
47. Sato M. Sato Y. Dynamic additive fuzzy clustering model Rizzi A. Vichi M. Bock H.H. Advances in Data Science and Classification 1998 118 124 Springer Berlin
48. 1-Norm and Related Methods 1987 417 426 North-Holland Amsterdam
49. Wang X. New similarity measures on fuzzy sets and on elements Fuzzy Sets and Systems 85 1997 305 309
50. Wang X. De Baets D. Kerre E. A comparative study of similarity measures Fuzzy Sets and Systems 73 1995 259 268
51. Windham M.P. Numerical classification of proximity data with assignment measures J. Classification 2 1985 157 172
52. Xie X.L. Beni G. A validity measure for fuzzy clustering IEEE Trans. Pattern Anal. Mach. Intell. 13 1991 841 847
53. Yang M.S. Convergence properties of the generalized fuzzy c-means clustering algorithms Comput. Math. Appl. 25 1993 3 11
54. Yang M.S. Ko C.H. On a class of fuzzy c-numbers clustering procedures for fuzzy data Fuzzy Sets and Systems 84 1996 49 60
55. Yang M.S. Liu H.H. Fuzzy clustering procedures for conical fuzzy vector data Fuzzy Sets and Systems 106 1999 189 200
56. Zadeh L.A. Fuzzy sets Inform. Control 8 1965 338 353
57. Zimmermann H.J. Fuzzy Set Theory and its Applications 1996 Kluwer Academic Press Dordrecht
58. Zwich, R., Carlstein, E., Budescu, D.V., 1987. Measures of similarity among fuzzy concepts: a comparative analysis. Internat. Approx. Reasoning 1, 221-242.