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Discounting and Combination Scheme in Evidence Theory for Dealing with Conflict in Information Fusion

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5861))

Abstract

Recently combination rules as well as the issue of conflict management in Dempster-Shafer theory have received considerable attention in information fusion research. Mostly these studies considered the combined mass assigned to the empty set as the conflict and have tried to provide alternatives to Dempster’s rule of combination, which mainly differ in the way of how to manage the conflict. In this paper, we introduce a hybrid measure to judge the difference between two bodies of evidence as a basis for conflict analysis, and argue that using the combined mass assigned to the empty set as a whole to quantify conflict seems inappropriate. We then propose to use the discounting operator in association with the combination operator to resolve conflict when combining evidence, in which the discount rate of a basic probability assignment is defined using the entropy of its corresponding pignistic probability function. Finally, an application of this discounting and combination scheme to fusion of decisions in classifier combination is demonstrated.

This work was supported by JSPS Grant-in-Aid for Scientific Research (C) #20500202.

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References

  1. Agirre, E., Edmonds, P. (eds.): Word Sense Disambiguation: Algorithms and Applications. Springer, Dordrecht (2006)

    Google Scholar 

  2. Al-Ani, A., Deriche, M.: A new technique for combining multiple classifiers using the Dempster–Shafer theory of evidence. J. Artif. Intell. Res. 17, 333–361 (2002)

    MATH  MathSciNet  Google Scholar 

  3. Bell, D., Guan, J.W., Bi, Y.: On combining classifiers mass functions for text categorization. IEEE Trans. Know. Data Eng. 17, 1307–1319 (2005)

    Article  Google Scholar 

  4. Chang, C.C., Lin, C.J.: LIBSVM: A library for support vector machines (2001), http://www.csie.ntu.edu.tw/cjlin/libsvm

  5. Delmotte, F., Smets, P.: Target identification based on the Transferable Belief Model interpretation of Dempster-Shafer model. IEEE Trans. Syst., Man, Cybern. A 34, 457–471 (2004)

    Article  Google Scholar 

  6. Dempster, A.P.: Upper and lower probabilities induced by a multi-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  7. Denoeux, T.: A neural network classifier based on Dempster-Shafer theory. IEEE Trans. Syst., Man, Cybern. A 30, 131–150 (2000)

    Article  Google Scholar 

  8. Denoeux, T.: A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Trans. Syst., Man, Cybern. 25, 804–813 (1995)

    Article  Google Scholar 

  9. Denoeux, T.: Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artif. Intell. 172, 234–264 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Comput. Intell. 4, 244–264 (1988)

    Article  Google Scholar 

  11. Grozea, C.: Finding optimal parameter settings for high performance word sense disambiguation. In: Proc. of ACL/SIGLEX Senseval-3, Barcelona, Spain, July 2004, pp. 125–128 (2004)

    Google Scholar 

  12. Ide, N., Véronis, J.: Introduction to the special issue on word sense disambiguation: The state of the art. Comput. Ling. 24, 1–40 (1998)

    Google Scholar 

  13. Josang, A.: The consensus operator for combining beliefs. Artif. Intell. 141, 157–170 (2002)

    Article  MathSciNet  Google Scholar 

  14. Jousselme, A.L., Liu, C., Grenier, D., Bosse, E.: Measuring ambiguity in the evidence theory. IEEE Trans. Syst., Man, Cybern. A 36, 890–903 (2006)

    Article  Google Scholar 

  15. Kilgarriff, A.: English lexical sample task description. In: Proc. of Senseval-2: Second Inter. Workshop on Evaluating Word Sense Disambiguation Syst., Toulouse, France, pp. 17–20 (2001)

    Google Scholar 

  16. Melamed, I.D., Resnik, P.: Tagger evaluation given hierarchical tag sets. Comp. and The Human. 34(1-2), 79–84 (2000)

    Article  Google Scholar 

  17. Mihalcea, R., Chklovski, T., Killgariff, A.: The Senseval-3 English lexical sample task. In: Proc. of ACL/SIGLEX Senseval-3, Barcelona, Spain, July 2004, pp. 25–28 (2004)

    Google Scholar 

  18. Huynh, V.-N., Nguyen, T.T., Le, C.A.: Adaptively entropy-based weighting classifiers in combination using Dempster-Shafer theory for word sense disambiguation. Comp. Speech Lang. (to appear)

    Google Scholar 

  19. Le, C.A., Huynh, V.-N., Shimazu, A., Nakamori, Y.: Combining classifiers for word sense disambiguation based on Dempster-Shafer theory and OWA operators. Data Know. Eng. 63, 381–396 (2007)

    Article  Google Scholar 

  20. Lee, Y.K., Ng, H.T.: An empirical evaluation of knowledge sources and learning algorithms for word sense disambiguation. In: Proc. of EMNLP, pp. 41–48 (2002)

    Google Scholar 

  21. Lefevre, E., Colot, O., Vannoorenberghe, P.: Belief function combination and conflict management. Infor. Fusion 3, 149–162 (2002)

    Article  Google Scholar 

  22. Lin, H.-T., Lin, C.-J., Weng, R.C.: A note on Platt’s probabilistic outputs for support vector machines. Mach. Learn. 68, 267–276 (2007)

    Article  Google Scholar 

  23. Haenni, R.: Are alternatives to Dempster’s rule of combination alternatives? Infor. Fusion 3, 237–241 (2002)

    Article  Google Scholar 

  24. Haenni, R.: Shedding new light on Zadeh’s criticism of Dempster’s rule of combination. In: FUSION 2005, 8th Inter. Conf. on Infor. Fusion, pp. 879–884 (2005)

    Google Scholar 

  25. Kittler, J., Hatef, M., Duin, R.P.W., Matas, J.: On combining classifiers. IEEE Trans. Patt. Anal. Mach. Intell. 20, 226–239 (1998)

    Article  Google Scholar 

  26. Liu, W.: Analysing the degree of conflict among belief functions. Artif. Intell. 170, 909–924 (2006)

    Article  MATH  Google Scholar 

  27. Murphy, C.: Combining belief functions when evidence conflicts. Dec. Sup. Syst. 29, 1–9 (2000)

    Article  Google Scholar 

  28. Platt, J.: Probabilistic outputs for support vector machines and comparison to regularized likelihood methods. In: Smola, A., Bartlett, P., Schölkopf, B., Schuurmans, D. (eds.) Advances in Large Margin Classifiers. MIT Press, Cambridge (2000)

    Google Scholar 

  29. Rogova, G.: Combining the results of several neural network classifiers. Neural Networks 7, 777–781 (1994)

    Article  Google Scholar 

  30. Ruspini, E.H., Lowrance, J.D., Strat, T.M.: Understanding evidential reasoning. Inter. J. Approx. Reason. 6, 401–424 (1992)

    Article  MATH  Google Scholar 

  31. Safranek, R.J., Gottschlich, S., Kak, A.C.: Evidence accumulation using binary frames of discerment for verification vision. IEEE Trans. Robot. Autom. 6, 405–417 (1990)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  33. Smets, P.: The combination of evidence in the transferable belief model. IEEE Trans. Patt. Anal. Mach. Intell. 12, 447–458 (1990)

    Article  Google Scholar 

  34. Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  35. Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Inter. J. Approx. Reason. 38, 133–147 (2004)

    Article  MathSciNet  Google Scholar 

  36. Smets, P.: Analyzing the combination of conflicting belief functions. Infor. Fusion 8, 387–412 (2007)

    Article  Google Scholar 

  37. Tsuruoka, Y.: A simple C++ library for maximum entropy classification (2006), http://www-tsujii.is.s.u-tokyo.ac.jp/~tsuruoka/maxent/

  38. Xu, L., Krzyzak, A., Suen, C.Y.: Several methods for combining multiple classifiers and their applications in handwritten character recognition. IEEE Trans. Syst., Man, Cybern. 22, 418–435 (1992)

    Article  Google Scholar 

  39. Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Infor. Sci. 41, 93–138 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  40. Yarowsky, D., Cucerzan, S., Florian, R., Schafer, C., Wicentowski, R.: The Johns Hopkins Senseval2 system descriptions. In: Proc. of SENSEVAL2, pp. 163–166 (2001)

    Google Scholar 

  41. Zadeh, L.A.: Reviews of Books: A Mathematical Theory of Evidence. AI Magazine 5, 81–83 (1984)

    Google Scholar 

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Authors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, 923-1292, Japan

    Van-Nam Huynh

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  1. Van-Nam Huynh
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Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

  3. Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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Huynh, VN. (2009). Discounting and Combination Scheme in Evidence Theory for Dealing with Conflict in Information Fusion. In: Torra, V., Narukawa, Y., Inuiguchi, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2009. Lecture Notes in Computer Science(), vol 5861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04820-3_20

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  • DOI: https://doi.org/10.1007/978-3-642-04820-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04819-7

  • Online ISBN: 978-3-642-04820-3

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