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A New Measure of Conflict and Hybrid Combination Rules in the Evidence Theory

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Artificial Intelligence and Soft Computing (ICAISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8468))

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Abstract

Based on the critical analysis of methods for evaluation of conflict between basic probability assignments (bpas) to be combined and combination rules in the Dempster-Shafer theory of evidence, a new simple, but reliable method for the evaluation of conflict between combining bpas is proposed and analysed. Using some critical examples, it is shown that the proposed approach performs better than Dempster’s rule and the known hybrid rule based on the weighted sum of conjunction and disjunction operators. It is shown that in the case of small conflict, the use of averaging rule for combination of bpas seems to be a best choice.

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References

  1. Delmotte, F., Dubois, L., Desodt, A., Borne, P.: Using trust in uncertainty theories. Information and Systems Engineering 1, 303–314 (1995)

    Google Scholar 

  2. Dubois, D., Prade, H.: A Set-Theoretic View on Belief Functions: Logical Operations and Approximations by Fuzzy Sets. International Journal of General Systems 12, 193–226 (1986)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  4. Dubois, D., Prade, H.: On the combination of evidence in various mathematical frameworks. In: Aamm, J., Luisi, T. (eds.) Reliability Data Collection and Analysis, pp. 213–241 (1992)

    Google Scholar 

  5. Florea, M.C., Dezert, J., Valin, P., Smarandache, F., Jousselme, A.L.: Adaptative combination rule and proportional conflict redistribution rule for information fusion. In: Proc. of Int. Conf. on Cognitive Systems with Interactive Sensors, Paris (2006), arXiv:cs/0604042v1

    Google Scholar 

  6. Florea, M.C., Jousselme, A.-L., Bossé, É., Grenier, D.: Robust combination rules for evidence theory. Information Fusion 10, 183–197 (2009)

    Article  Google Scholar 

  7. Florea, M.C., Bossé, É.: Crisis Management Using Dempster-Shafer Theory: Using Dissimilarity Measures to Characterize Source’s Reliability. In: Conference NATO RTO IST-086, Bucharest, May 11-12 (2009), http://ftp.rta.nato.int/public//PubFullText/RTO/MP/RTO-MP-IST-086///MP-IST-086-17.pdf

  8. Haenni, R.: Are alternatives to Dempster’s rule of combination real alternatives?: Comments on “about the belief function combination and the conflict management problem”-Lefevre et al. Information Fusion 3, 237–239 (2002)

    Article  Google Scholar 

  9. Horiuchi, T.: Decision Rule for Pattern Classification by Integrating Interval Feature Value. IEEE Trans. Pattern Analysis and Machine Intelligence 20, 440–448 (1998)

    Article  MathSciNet  Google Scholar 

  10. Inagaki, T.: Interdependence between Safety-Control Policy and Multiple-Sensor Schemes Via Dempster-Shafer Theory. IEEE Transactions on Reliability 40, 182–188 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Josang, A.: The consensus operator for combining beliefs. Artificial Intelligence 141, 157–170 (2002)

    Article  MathSciNet  Google Scholar 

  12. Josang, A., Daniel, M., Vannoorenberghe, P.: Strategies for Combining Conflicting Dogmatic Beliefs. In: Proceedings of 6th International Conference on International Fusion, vol. 2, pp. 1133–1140 (2003)

    Google Scholar 

  13. Jousselme, A.-L., Grenier, D., Bosse, E.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)

    Article  Google Scholar 

  14. Jousselme, A.-L., Maupin, P.: Distances in evidence theory: Comprehensive survey and generalisations. International Journal of Approximate Reasoning 53, 118–145 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Liu, W.: Analizing the degree of conflict among belief functions. Artificial Intelligence 170, 909–924 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Martin, A., Jousselme, A.-L., Osswald, C.: Conflict measure for the discounting operation on belief functions. In: Proc. of the 11th International Conference on Information Fusion, Cologne, Germany, pp. 1003–1010 (2008)

    Google Scholar 

  17. Martin, A., Osswald, C.H., Dezert, J., Smarandache, F.: General Combination Rules for Qualitative and Quantitative Beliefs. Journal of Advances in Information Fusion 3, 67–89 (2008)

    Google Scholar 

  18. Matsuyama, T.: Belief Formation From Observation and Belief Integration Using Virtual Belief Space in Dempster-Shafer Probability Model. In: Proc. Multisensor Fusion and Integration for Intelligent Systems (MFI 1994), pp. 379–386 (1994)

    Google Scholar 

  19. Murphy, C.K.: Combining Belief Functions When Evidence Conflicts. Decision Support Systems 29, 1–9 (2000)

    Article  Google Scholar 

  20. Sentz, K., Ferson, S.: Combination of Evidence in Dempster-Shafer Theory. Sandia National Laboratories SAND, 2002-0835 (2002)

    Google Scholar 

  21. Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    Google Scholar 

  22. Smarandache, F.: An In-Depth Look at Information Fusion Rules and the Unification of Fusion Theories. In: Computing Research Repository (CoRR), vol. cs.OH/0410033, Cornell University arXiv (2004)

    Google Scholar 

  23. Smarandache, F.: Unification of Fusion Theories (UFT), May 16-27. NATO Advanced Study Institute, Albena (2005)

    Google Scholar 

  24. Smets, P.: The combination of evidence in the transferable belief model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 447–458 (1990)

    Article  Google Scholar 

  25. Smets, P.: The alpha-junctions: combination operators applicable to belief functions. In: Nonnengart, A., Kruse, R., Ohlbach, H.J., Gabbay, D.M. (eds.) FAPR 1997 and ECSQARU 1997. LNCS, vol. 1244, pp. 131–153. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  26. Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. International Journal of Approximate Reasoning 38, 133–147 (2004)

    Article  MathSciNet  Google Scholar 

  27. Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Information Sciences 41, 93–138 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  29. Zadeh, L.: A simple view of the Dempster-Shafer theory of evidence and its application for the rule of combination. AI Magazine 7, 85–90 (1986)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Comp.& Information Sci., Czestochowa University of Technology, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Ludmila Dymova, Pavel Sevastjanov & Kamil Tkacz

  2. Mogilev State A. Kuleshov University, Kosmonavtov str., 1, Mogilev, 212022, Mogilev, Belarus

    Tatyana Cheherava

Authors
  1. Ludmila Dymova
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  2. Pavel Sevastjanov
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  3. Kamil Tkacz
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  4. Tatyana Cheherava
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Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski  & Rafał Scherer  & 

  2. Częstochowa University of Technology, 42-200, Częstochowa, Poland

    Marcin Korytkowski

  3. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Computer Science Division, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  5. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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© 2014 Springer International Publishing Switzerland

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Dymova, L., Sevastjanov, P., Tkacz, K., Cheherava, T. (2014). A New Measure of Conflict and Hybrid Combination Rules in the Evidence Theory. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8468. Springer, Cham. https://doi.org/10.1007/978-3-319-07176-3_36

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  • DOI: https://doi.org/10.1007/978-3-319-07176-3_36

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07175-6

  • Online ISBN: 978-3-319-07176-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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