A Distance-Based Decision in the Credal Level

  • Amira Essaid
  • Arnaud Martin
  • Grégory Smits
  • Boutheina Ben Yaghlane
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8884)


Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the most likely hypothesis. Others allow that a decision is made on a set of hypotheses. In [6], we proposed a decision rule based on a distance measure. First, in this paper, we aim to demonstrate that our proposed decision rule is a particular case of the rule proposed in [4]. Second, we give experiments showing that our rule is able to decide on a set of hypotheses. Some experiments are handled on a set of mass functions generated randomly, others on real databases.


belief function theory imprecise decision distance 


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  1. 1.
    Appriou, A.: Approche générique de la gestion de l’incertain dans les processus de fusion multisenseur. Traitement du Signal 22, 307–319 (2005)zbMATHGoogle Scholar
  2. 2.
    Dempster, A.P.: Upper and Lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Denoeux, T.: A k-nearest neighbor classification rule based on Dempster-Shafer Theory. IEEE Transactions on Systems, Man, and Cybernetics 25(5), 804–813 (1995)CrossRefGoogle Scholar
  4. 4.
    Denoeux, T.: Analysis of evidence-theoric decision rules for pattern classification. Pattern Recognition 30(7), 1095–1107 (1997)CrossRefGoogle Scholar
  5. 5.
    Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4, 244–264 (1988)CrossRefGoogle Scholar
  6. 6.
    Essaid, A., Martin, A., Smits, G., Ben Yaghlane, B.: Uncertainty in ontology matching: a decision rule based approach. In: Proceeding of the International Conference on Information Processing and Mangement Uncertainty, pp. 46–55 (2014)Google Scholar
  7. 7.
    Jousselme, A.L., Grenier, D., Bossé, E.: A New Distance Between Two Bodies of Evidence. Information Fusion 2, 91–101 (2001)CrossRefGoogle Scholar
  8. 8.
    Martin, A., Quidu, I.: Decision support with belief functions theory for seabed characterization. In: Proceeding of the International Conference on Information Fusion, pp. 1–8 (2008)Google Scholar
  9. 9.
    Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)Google Scholar
  10. 10.
    Smets, P.: The Combination of Evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(5), 447–458 (1990)CrossRefGoogle Scholar
  11. 11.
    Smets, P.: Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9(1), 1–35 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Smets, P., Kennes, R.: The Transferable Belief Model. Artificial Intelligent 66, 191–234 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Information Sciences 41, 93–137 (1987)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Amira Essaid
    • 1
    • 2
  • Arnaud Martin
    • 2
  • Grégory Smits
    • 2
  • Boutheina Ben Yaghlane
    • 3
  1. 1.ISG TunisLARODEC, University of TunisTunisia
  2. 2.IRISAUniversity of Rennes1LannionFrance
  3. 3.IHEC CarthageLARODEC, University of CarthageTunisia

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