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Reasoning under Uncertainty in the AHP Method Using the Belief Function Theory

  • Amel Ennaceur
  • Zied Elouedi
  • Eric Lefevre
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

The Analytic Hierarchy Process (AHP) method was introduced to help the decision maker to express judgments on alternatives over a number of criteria. In this paper, our proposal extends the AHP method to an uncertain environment, where the uncertainty is represented through the Transferable Belief Model (TBM), one interpretation of the belief function theory. In fact, we suggest a novel framework that tackles the challenge of introducing uncertainty in both the criterion and the alternative levels, where the objective is to represent imperfection that may appear in the pair-wise comparisons and to model the relationship between these alternatives and criteria through conditional beliefs.

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References

  1. 1.
    Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence: An alternative approach to multicriteria decision modelling. Omega 28(1), 37–50 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brans, J.P., Vincke, P., Marechal, B.: How to select and how to rank projects: The PROMOTEE method. European Journal of Operational Research 24, 228–238 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Dezert, J., Tacnet, J.M., Batton-Hubert, M., Smarandache, F.: Multi-Criteria Decision Making based on DSmT-AHP. In: Workshop on the Theory of Belief Functions (2010)Google Scholar
  4. 4.
    Ennaceur, A., Elouedi, Z., Lefevre, E.: Handling Partial Preferences in the Belief AHP Method: Application to Life Cycle Assessment. In: Pirrone, R., Sorbello, F. (eds.) AI*IA 2011. LNCS (LNAI), vol. 6934, pp. 395–400. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: state of the art surveys. Springers International Series in Operations Research and Management Science, vol. 4 (2005)Google Scholar
  6. 6.
    Keeney, R.L., Raiffa, H.: Decisions with multiple objectives: Preferences and value tradeoffs. Cambridge University Press (1976)Google Scholar
  7. 7.
    Laarhoven, P.V., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems 11, 199–227 (1983)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Saaty, T.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 234–281 (1977)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Saaty, T.: The Analytic Hierarchy Process. McGraw-Hill, New-York (1980)zbMATHGoogle Scholar
  10. 10.
    Schoner, B., Wedley, W.C.: Ambiguous criteria weights in AHP: consequences and solutions. Decision Sciences 20, 462–475 (1989)CrossRefGoogle Scholar
  11. 11.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
  12. 12.
    Smets, P.: Belief functions: the disjunctive rule of combination and the generalized bayesian theorem. International Journal of Approximate Reasoning 9, 1–35 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Smets, P.: The combination of evidence in the Transferable Belief Model. IEEE Pattern Analysis and Machine Intelligence, 447–458 (1990)Google Scholar
  14. 14.
    Smets, P., Kennes, R.: The Transferable Belief Model. Artificial Intelligence 66, 191–234 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Triantaphyllou, E.: Multi-Criteria Decision Making methods: a comparative study. Kluwer Academic Publishers (2000)Google Scholar
  16. 16.
    Utkin, L.V.: A new ranking procedure by incomplete pairwise comparisons using preference subsets. Intelligent Data Analysis 13(2), 229–241 (2009)MathSciNetGoogle Scholar
  17. 17.
    Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill Book Company (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amel Ennaceur
    • 1
  • Zied Elouedi
    • 1
  • Eric Lefevre
    • 2
  1. 1.LARODECUniversity of Tunis, Institut Supérieur de GestionTunisTunisia
  2. 2.UArtois EA 3926 LGI2AUniv. Lille Nord of FranceLilleFrance

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