Fuzzy Time Arrays and Dissimilarity Measures For Fuzzy Time Trajectories

  • Renato Coppi
  • Pierpaolo D’Urso
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In this paper we define a fuzzy extension of a time array. The algebraic and geometric characteristics of the fuzzy time array are analyzed. Furthermore, considering the objects space ℜ J+1, where J is the number of variables and the remaining dimension is related to time, we suggest different dissimilarity measures for fuzzy time trajectories.


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  1. CARLIER, A. (1986): Factor Analysis of Evolution and Cluster Methods on Trajectories. In: F. De Antoni, N. Lauro, and A. Rizzi (Eds.): Proceedings in Computational Statistics (COMPSTAT), Physica-Verlag, Heidelberg, 140–145.Google Scholar
  2. CARLIER, A. (1991): About Distances for Clustering Longitudinal Multivariate Data, Proceedings of the Third Conference of the IFCS, Edinburgh, Scotland.Google Scholar
  3. CARLIER, A. (1999): Distances Between Trajectories for Longitudinal Data, Proceedings of the Conference of the VOC, Leiden, The Netherlands.Google Scholar
  4. COPPI, R. and D’URSO, P. (1999): The Geometric Approach to the Comparison of Multivariate Time Trajectories,Proceedings of the Conference of the CLAD AGSIS, Rome, 5–6 July, 1999, 177–180.Google Scholar
  5. D’URSO, P. (1999): Fuzzy Classification for Time Arrays, PhD Thesis, University “La Sapienza”, Rome, Italy (in Italian).Google Scholar
  6. D’URSO, P. and VICHI, M. (1998): Dissimilarities Between Trajectories of a Three-Way Longitudinal Data Set. In: A. Rizzi, M. Vichi, and H.-H. Bock (Eds.): Advances in Data Science and Classification, Springer, Heidelberg, 585–592.Google Scholar
  7. HARSHMAN, R. A. and LUNDY, M. E. (1984): Data Extended PARAFAC Model. In: H. G. Law, C. W. Snyder, Jr, J. A. Hattie and R. P. McDonald (Eds.): Research Methods for Multimode Data Analysis, Praeger, New York, 216–284.Google Scholar
  8. HARTIGAN, J.A. (1975): Clustering Algoritms, John Wiley & Sons, New York.Google Scholar
  9. RIZZI, A. and VICHI, M. (1995): Representations, Synthesis, Variability and Data Preprocessing of a Three-way Data Set, Computational Statistics & Data Analysis, 19, 203–222.CrossRefGoogle Scholar
  10. SAPORTA, G. and LAVALLARD, F. (1996): L’Analyse des Données Évolutives Méthodes et Applications. Éditions Technip, Paris.Google Scholar
  11. ZADEH, L. A. (1965): Fuzzy Sets, Informat. Control, 8, 338–353.CrossRefGoogle Scholar
  12. ZIMMERMANN, H. J. (1991): Fuzzy Set Theory and its Application, Kluwer AcademicGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • Renato Coppi
    • 1
  • Pierpaolo D’Urso
    • 1
  1. 1.Dipartimento di Statistica, Probabilitá e Statistiche ApplicateUniversitá di Roma ”La Sapienza”RomaItaly

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