Advertisement

Possibilistic Conditional Preference Networks

  • Nahla Ben Amor
  • Didier Dubois
  • Héla GouiderEmail author
  • Henri Prade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9161)

Abstract

The paper discusses the use of product-based possibilistic networks for representing conditional preference statements on discrete variables. The approach uses non-instantiated possibility weights to define conditional preference tables. Moreover, additional information about the relative strengths of symbolic weights can be taken into account. It yields a partial preference order among possible choices corresponding to a symmetric form of Pareto ordering. In the case of Boolean variables, this partial ordering coincides with the inclusion between the sets of preference statements that are violated. Furthermore, this graphical model has two logical counterparts in terms of possibilistic logic and penalty logic. The flexibility and the representational power of the approach are stressed. Besides, algorithms for handling optimization and dominance queries are provided.

References

  1. 1.
    Ben Amor, N., Dubois, D., Gouider, H., Prade, H.: Possibilistic networks: a new setting for modeling preferences. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS, vol. 8720, pp. 1–7. Springer, Heidelberg (2014) Google Scholar
  2. 2.
    Ben Amor, N., Benferhat, S., Mellouli, K.: Anytime possibilistic propagation algorithm. In: Proceedings of the 1st International Conference Computing in an Imperfect World, pp. 263–279 (2002)Google Scholar
  3. 3.
    Benferhat, S., Dubois, D., Garcia, L., Prade, H.: On the transformation between possibilistic logic bases and possibilistic causal networks. Int. J. Approx. Reasoning 29(2), 135–173 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boutilier, C., Brafman, R.I.: A tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artif. Intell. Res. 21, 135–191 (2004)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Brafman, R.I., Domshlak, C.: Introducing Variable Importance Tradeoffs Into CP-nets. CoRR, New York (2013) Google Scholar
  6. 6.
    Dawid, A.P.: Applications of a general propagation algorithm for probabilistic expert systems. Stat. Comput. 2(1), 25–36 (1992)CrossRefGoogle Scholar
  7. 7.
    Dupin de Saint-Cyr, F., Lang, J., Schiex, T.: Penalty logic and its link with Dempster-Shafer theory. In: Proceedings of the 10th Conference UAI, pp. 204–211, Morgan Kaufmann (1994)Google Scholar
  8. 8.
    Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144(1), 3–23 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dubois, D., Prade, H., Touazi, F.: Conditional Preference-nets, possibilistic logic, and the transitivity of priorities. In: Proceedings of the 33rd SGAI Intenational Conference, pp. 175–184. Springer, Heidelberg (2013)Google Scholar
  10. 10.
    Goldsmith, J., Lang, J., Truszczynski, M., Wilson, N.: The computational complexity of dominance and consistency in CP-nets. J. Artif. Intell. Res. 33, 403–432 (2008)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Gonzales, C., Perny, N.: GAI networks for utility elicitation. In: Proceedings of the 9th International Conference Principles of Knowledge Representation and Reasoning, pp. 224–234 (2004)Google Scholar
  12. 12.
    Jensen, F.V., Lauritzen, S.L., Olesen, K.G.: Bayesian updating in causal probabilistic networks by local computations. Comput. Stat. Q. 4, 269–282 (1990)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Nilsson, D.: An efficient algorithm for finding the m most probable configurations in probabilistic expert systems. Stat. Comput. 8(2), 159–173 (1998)CrossRefGoogle Scholar
  14. 14.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmman, San Francisco (1988) zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nahla Ben Amor
    • 1
  • Didier Dubois
    • 2
  • Héla Gouider
    • 1
    Email author
  • Henri Prade
    • 2
  1. 1.LARODECInstitut Supérieur de Gestion TunisLe BardoTunisie
  2. 2.IRIT – CNRSToulouseFrance

Personalised recommendations