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The First Belief Dominance: A New Approach in Evidence Theory for Comparing Basic Belief Assignments

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Algorithmic Decision Theory (ADT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5783))

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Abstract

In this paper, we consider problems where the data is uncertain and/or imprecise and given by basic belief assignments (BBA’s). In order to compare the different pairs of the BBA’s, a new concept called the first belief dominance is proposed. This is naturally inspired by the concept of first stochastic dominance that allows comparing probability distributions. Finally, an application in multicriteria decision aid context is presented to illustrate the proposed technique.

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References

  1. Aregui, A., Denoeux, T.: Fusion of one-class classifiers in the belief function framework. In: Proceedings of the 10th International Conference on Information Fusion, Quebec, Canada (2007)

    Google Scholar 

  2. Aregui, A., Denoeux, T.: Novelty detection in the belief functions framework. In: Proceedings of IPMU 2006, Paris (2006)

    Google Scholar 

  3. Bawa, V.S.: Stochastic dominance: A research bibliography. Management Science 28, 698–712 (1982)

    Article  MathSciNet  Google Scholar 

  4. Ben Amor, S., Jabeur, K., Martel, J.M.: Multiple criteria aggregation procedure for mixed evaluations. European Journal of Operational Research 181, 1506–1515 (2007)

    Article  Google Scholar 

  5. Dempster, A.P.: Upper and lower probabilities induced by a multi-valued mapping. Annual Mathematics and Statistics 38, 325–339 (1967)

    Article  Google Scholar 

  6. Denoeux, T.: Extending stochastic ordering to belief functions on the real line. Information Sciences 179, 1362–1376 (2009)

    Article  MathSciNet  Google Scholar 

  7. Hadar, J., Russell, W.R.: Rules for Ordering Uncertain Prospects. The American Economic Review 59, 25–34 (1969)

    Google Scholar 

  8. Hanoch, G., Levy, H.: The efficiency analysis of choices involving risk. Review of Economic Studies 36, 335–346 (1969)

    Article  Google Scholar 

  9. Jabeur, K., Martel, J.M.: A collective choice method based on individual preferences relational systems (p.r.s.). European Journal of Operational Research 177, 469–485 (2005)

    MathSciNet  MATH  Google Scholar 

  10. Jabeur, K., Martel, J.M.: An ordinal sorting method for group decision-making. European Journal of Operational Research 177, 1549–1565 (2007)

    Article  MathSciNet  Google Scholar 

  11. Jabeur, K., Martel, J.M.: Détermination d’un (ou plusieurs) systèmes(s) relationnel(s) de préférence (s.r.p) collectif(s) à partir des s.r.p individuels. Document de travail # 011-2002, Faculté des Sciences de l’Administration (FSA), Université Laval (2002)

    Google Scholar 

  12. Langewish, A., Choobineh, F.: Stochastic dominance tests for ranking alternatives under ambiguity. European Journal of Operational Research 95, 139–154 (1996)

    Article  Google Scholar 

  13. Lehmann, E.: Ordered families of distributions. Annals of Mathematical Statistics 26, 399–419 (1955)

    Article  MathSciNet  Google Scholar 

  14. Mann, H.B., Whitney, D.R.: On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics 18, 50–60 (1947)

    Article  MathSciNet  Google Scholar 

  15. Martel, J.M., Zaras, K.: Stochastic dominance in multicriterion analysis under risk. Theory and Decision 39, 31–49 (1995)

    Article  Google Scholar 

  16. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  17. Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)

    Article  MathSciNet  Google Scholar 

  18. Smets, P.: Decision Making in the TBM: the Necessity of the Pignistic Transformation. International Journal of Approximate Reasoning 38, 133–147 (2005)

    Article  MathSciNet  Google Scholar 

  19. Vincke, P.: L’Aide Multicritère à la Décision. Editions de l’Université de Bruxelles, Editions Ellipses, Bruxelles (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculté des sciences économiques et de gestion de Sfax, Université de Sfax, Sfax, Tunisie

    Mohamed Ayman Boujelben & Habib Chabchoub

  2. Faculté des sciences appliquées, Université Libre de Bruxelles, Bruxelles, Belgique, Belgium

    Yves De Smet

  3. Institut supérieur de gestion industrielle de Sfax, Université de Sfax, Sfax, Tunisie

    Ahmed Frikha

Authors
  1. Mohamed Ayman Boujelben
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  2. Yves De Smet
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  3. Ahmed Frikha
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  4. Habib Chabchoub
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Editor information

Editors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

  2. LAMSADE-CNRS, University of Paris Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Alexis Tsoukias

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© 2009 Springer-Verlag Berlin Heidelberg

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Boujelben, M.A., De Smet, Y., Frikha, A., Chabchoub, H. (2009). The First Belief Dominance: A New Approach in Evidence Theory for Comparing Basic Belief Assignments. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_24

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  • DOI: https://doi.org/10.1007/978-3-642-04428-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04427-4

  • Online ISBN: 978-3-642-04428-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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