A Family of Divergences between φ-Probabilistic Sets with Application to Handshape Recognition

  • Juan M. León-Rojas
  • José Moreno
  • Antonio Silva
  • Montaña Morales
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


We introduce a family of divergences between φ-probabilistic sets, with real supports. The supports are never unbounded to opposite sides. We start from weighted and percentiled dissimilarities between arbitrary unions of compact intervals of real numbers. As an application we model the problem of the recognition of a handshape as a metric problem between φ-probabilistic sets. The proposed family of divergences is a suitable solution to this problem of comparing one handshape prototype, a φ-probabilistic set, with one input handshape, a φ-fuzzy set.


  1. 1.
    Bezdek, J.: Fuzzy models. What are they, and why? IEEE Transactions on Fuzzy Systems 1(1) (1993) 1–6MathSciNetGoogle Scholar
  2. 2.
    Zadeh, L. A.: Similarity relations and fuzzy orderings. Information Sciences 3(2) (1971) 177–200zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Klir, G. J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall PTR, Upper Saddle River, New Jersey (1995)Google Scholar
  4. 4.
    Calot, G.: Cours de Statistique Descriptive. Dunod, Paris (1965)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: A unifying view of comparison indices in a fuzzy set-theoretic framework. In: Yager, R. R. (ed.): Fuzzy Set and Possibility Theory. Recent Developments. Pergamon Press, New York (1982)Google Scholar
  6. 6.
    Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware & Soft Computing 2 (1995) 71–84zbMATHMathSciNetGoogle Scholar
  7. 7.
    Sambuc, R. Fonctions φ-Floues. Application á l’Aide au Diagnostic en Pathologie Thyroïdienne. PhD Thesis, Faculty of Medicine of Marseille (1975)Google Scholar
  8. 8.
    Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Academic Press, New York (1975)zbMATHGoogle Scholar
  9. 9.
    Kaufmann, A.: Les Expertons. Hermes, Paris (1987)zbMATHGoogle Scholar
  10. 10.
    Moreno J., León-Rojas, J. M., Silva, A.: Sistema de traducción automática del Lenguaje de Signos Español al Español oral. Novática 136 (1998) 60–64Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Juan M. León-Rojas
    • 1
  • José Moreno
    • 2
  • Antonio Silva
    • 2
  • Montaña Morales
    • 3
  1. 1.Department of MathematicsUniversity of ExtremaduraCáceresSpain
  2. 2.Computer Science DepartmentUniversity of ExtremaduraCáceresSpain
  3. 3.Computer Science DepartmentMinistery of Education and Culture, I. E. S. ÁgoraCáceresSpain

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