Probability-Possibility Transformation:

Application to Bayesian and Possibilistic Networks
  • Yosra Ben Slimen
  • Raouia Ayachi
  • Nahla Ben Amor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)


Probability-possibility transformation is a purely mechanical transformation of probabilistic support to possibilistic support and vice versa. In this paper, we apply the most common transformations to graphical models, i.e., Bayesian into possibilistic networks. We show that existing transformations are not appropriate to transform Bayesian networks to possibilistic ones since they cannot preserve the information incorporated in joint distributions. Therefore, we propose new consitency properties, exclusively useful for graphical models transformations.


Probability-Possibility transformation Bayesian networks Possibilistic networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ayachi, R., Ben Amor, N., Benferhat, S.: Possibilistic local structure for compiling min-based networks. In: SMPS, pp. 479–487 (2012)Google Scholar
  2. 2.
    Borgelt, C., Gebhardt, J., Kruse, R.: Possibilistic graphical models. In: Proceedings of the International School for the Synthesis of Expert Knowledge (1998)Google Scholar
  3. 3.
    Bouguelid, M.S.: Contribution à l’application de la reconnaissance des formes et la théorie des possibilités au diagnostic adaptatif et prédictif des systèmes dynamiques. PhD thesis, Université de Reims Champaghe-Ardenne (Décembre 2007)Google Scholar
  4. 4.
    Dubois, D., Foulloy, L., Mauris, G., Prade, H.: Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities. Reliable Computing (2004)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Possibility theory: An approach to computerized, Processing of uncertainty. Plenium Press, New York (1988)CrossRefzbMATHGoogle Scholar
  7. 7.
    Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. Fuzzy Logic (1993)Google Scholar
  8. 8.
    Dubois, D., Prade, H., Smets, P.: A definition of subjective possibility. International Journal of Approximate Reasoning 48, 352–364 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Klir, G.J.: Probability-possibility transformations: a comparison. Int. J. General Systems 21, 291–310 (1992)CrossRefzbMATHGoogle Scholar
  10. 10.
    Klir, G.J.: Information-preserving probability-possibility transformations: recent developments. Fuzzy Logic, 417–428 (1993)Google Scholar
  11. 11.
    Mouchaweh, M.S.: Diagnosis in real time for evolutionary processes using pattern recognition and possibility theory. Invited paper in International Journal of Computational Cognition, 79–112 (2004)Google Scholar
  12. 12.
    Mouchaweh, M.S., Bouguelid, M.S., Billaudel, P., Riera, B.: Variable probability-possibility transformation. In: 25th European Annual Conference on Human Decision-Making and Manual Control (EAM 2006), pp. 417–428 (September 2006)Google Scholar
  13. 13.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)Google Scholar
  14. 14.
    Zadeh, L.A.: Fuzzy sets as a biaisis for a therory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Yosra Ben Slimen
    • 1
  • Raouia Ayachi
    • 1
  • Nahla Ben Amor
    • 1
  1. 1.Institut Supérieur de Gestion TunisLARODECLe BardoTunisie

Personalised recommendations