Solving Multi-criteria Decision Problems under Possibilistic Uncertainty Using Optimistic and Pessimistic Utilities

  • Nahla Ben Amor
  • Fatma Essghaier
  • Hélène Fargier
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 444)


This paper proposes a qualitative approach to solve multi-criteria decision making problems under possibilistic uncertainty. Depending on the decision maker attitude with respect to uncertainty (i.e. optimistic or pessimistic) and on her attitude with respect to criteria (i.e. conjunctive or disjunctive), four ex-ante and four ex-post decision rules are defined and investigated. In particular, their coherence w.r.t. the principle of monotonicity, that allows Dynamic Programming is studied.


Dynamic Program Algorithm Weak Monotonicity Possibility Degree Compound Lottery Simple Lottery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dubois, D., Marichal, J.L., Prade, H., Roubens, M., Sabbadin, R.: The use of the discrete sugeno integral in decision-making: A survey. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9(5), 539–561 (2001)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: Weighted minimum and maximum operations in fuzzy set theory. Journal of Information Sciences 39, 205–210 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Possibility theory as a basis for qualitative decision theory. In: Proceedings of IJCAI, pp. 1924–1930 (1995)Google Scholar
  4. 4.
    Fargier, H., Ben Amor, N., Guezguez, W.: On the complexity of decision making in possibilistic decision trees. In: Conference on UAI, pp. 203–210 (2011)Google Scholar
  5. 5.
    Garcias, L., Sabbadin, R.: Possibilistic influence diagrams. In: Proceedings of ECAI, pp. 372–376 (2006)Google Scholar
  6. 6.
    Guezguez, W., Ben Amor, N., Mellouli, K.: Qualitative possibilistic influence diagrams based on qualitative possibilistic utilities. EJOR 195, 223–238 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Harsanyi, J.C.: Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy 63(4), 309–321 (1955)CrossRefGoogle Scholar
  8. 8.
    Marichal, J.L.: An axiomatic approach of the discrete sugeno integral as a tool to aggregate interacting criteria in a qualitative framework. IEEE T. on Fuzzy Systems 9(1), 164–172 (2001)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Morgenstern, O., Neumann, J.V.: Theory of Games and Economic Behavior, 2nd edn. Princeton University Press (1947)Google Scholar
  10. 10.
    Myerson, R.B.: Utilitarianism, egalitarianism, and the timing effect in social choice problems. Econometrica 49(4), 883–897 (1981)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Sabbadin, R.: Empirical comparison of probabilistic and possibilistic markov decision processes algorithms. In: Proceedings of European Conference on Artificial Intelligence, pp. 586–590 (2000)Google Scholar
  12. 12.
    Sabbadin, R.: Possibilistic markov decision processes. Engineering Applications of Artificial Intelligence 14, 287–300 (2001)CrossRefGoogle Scholar
  13. 13.
    Sugeno, M.: Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology (1974)Google Scholar
  14. 14.
    Whalen, T.: Decision making under uncertainty with various assumptions about available information. IEEE T. on SMC 14, 888–900 (1984)MathSciNetGoogle Scholar
  15. 15.
    Yager, R.: Possibilistic decision making. IEEE T. on SMC 9, 388–392 (1979)MathSciNetGoogle Scholar
  16. 16.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nahla Ben Amor
    • 1
  • Fatma Essghaier
    • 1
    • 2
  • Hélène Fargier
    • 2
  1. 1.LARODECInstitut Supérieur de Gestion TunisTunisie
  2. 2.IRIT-CNRS, UMR 5505Université de ToulouseFrance

Personalised recommendations