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Belief Functions and Degrees of Non-conflictness

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

Abstract

A hidden conflict of belief functions in the case where the sum of all multiples of conflicting belief masses being equal to zero was observed. To handle that, degrees of non-conflictness and full non-conflictness are defined. The family of these degrees of non-conflictness is analyzed, including its relation to full non-conflictness. Further, mutual non-conflictness between two belief functions accepting internal conflicts of individual belief functions are distinguished from global non-conflictness excluding both mutual conflict between belief functions and also all internal conflicts of individual belief functions. Finally, both theoretical and computational issues are presented.

Supported by grant GAČR no. 19-04579S.

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Notes

  1. 1.

    Conflicting and non-conflicting parts of belief functions originally come from [5].

  2. 2.

    Plausibility of singletons is called contour function by Shafer in [19], thus \(Pl{\_P}(Bel)\) is a normalization of contour function in fact.

References

  1. Burger, T.: Geometric views on conflicting mass functions: from distances to angles. Int. J. Approximate Reasoning 70, 36–50 (2016)

    Article  MathSciNet  Google Scholar 

  2. Cobb, B.R., Shenoy, P.P.: On the plausibility transformation method for translating belief function models to probability models. Int. J. Approximate Reasoning 41(3), 314–330 (2006)

    Article  MathSciNet  Google Scholar 

  3. Daniel, M.: Probabilistic transformations of belief functions. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 539–551. Springer, Heidelberg (2005). https://doi.org/10.1007/11518655_46

    Chapter  Google Scholar 

  4. Daniel, M.: Conflicts within and between belief functions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 696–705. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14049-5_71

    Chapter  Google Scholar 

  5. Daniel, M.: Non-conflicting and conflicting parts of belief functions. In: 7th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2011), pp. 149–158. SIPTA, Innsbruck (2011)

    Google Scholar 

  6. Daniel, M.: Properties of plausibility conflict of belief functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7894, pp. 235–246. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38658-9_22

    Chapter  Google Scholar 

  7. Daniel, M.: Conflict between belief functions: a new measure based on their non-conflicting parts. In: Cuzzolin, F. (ed.) BELIEF 2014. LNCS (LNAI), vol. 8764, pp. 321–330. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11191-9_35

    Chapter  Google Scholar 

  8. Daniel, M., Kratochvíl, V.: Hidden auto-conflict in the theory of belief functions. In: Proceedings of the 20th Czech-Japan Seminar on Data Analysis and Decision Making Under Uncertainty, pp. 34–45 (2017)

    Google Scholar 

  9. Daniel, M., Kratochvíl, V.: On hidden conflict of belief functions. In: Proceedings of EUSFLAT 2019 (2019, in print)

    Google Scholar 

  10. Daniel, M., Ma, J.: Conflicts of belief functions: continuity and frame resizement. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS (LNAI), vol. 8720, pp. 106–119. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11508-5_10

    Chapter  Google Scholar 

  11. Destercke, S., Burger, T.: Toward an axiomatic definition of conflict between belief functions. IEEE Trans. Cybern. 43(2), 585–596 (2013)

    Article  Google Scholar 

  12. Dowle, M., Srinivasan, A.: data.table: extension of ‘data.frame’ (2016). https://CRAN.R-project.org/package=data.table, r package version 1.10.0

  13. Lefèvre, E., Elouedi, Z.: How to preserve the conflict as an alarm in the combination of belief functions? Decis. Support Syst. 56, 326–333 (2013)

    Article  Google Scholar 

  14. Liu, W.: Analyzing the degree of conflict among belief functions. Artif. Intell. 170(11), 909–924 (2006)

    Article  MathSciNet  Google Scholar 

  15. Martin, A.: About conflict in the theory of belief functions. In: Denoeux, T., Masson, M.H. (eds.) Belief Functions: Theory and Applications, pp. 161–168. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29461-7_19

    Chapter  Google Scholar 

  16. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2016). https://www.R-project.org/

  17. RStudio Team: RStudio: Integrated Development Environment for R. RStudio Inc., Boston (2015). http://www.rstudio.com/

  18. Schubert, J.: The internal conflict of a belief function. In: Denoeux, T., Masson, M.H. (eds.) Belief Functions: Theory and Applications, pp. 169–177. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Shafer, G.: A Mathematical Theory of Evidence, vol. 1. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  20. Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approximate Reasoning 38(2), 133–147 (2005)

    Article  MathSciNet  Google Scholar 

  21. Smets, P.: Analyzing the combination of conflicting belief functions. Inf. Fusion 8(4), 387–412 (2007)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Jan Becher - Karlovarská Becherovka, a.s., Pernod Ricard Group, Přemyslovská 43, 130 00, Prague 3, Czech Republic

    Milan Daniel

  2. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou veží 4, 182 08, Prague 8, Czech Republic

    Václav Kratochvíl

Authors
  1. Milan Daniel
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  2. Václav Kratochvíl
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Correspondence to Milan Daniel .

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Editors and Affiliations

  1. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Daniel, M., Kratochvíl, V. (2019). Belief Functions and Degrees of Non-conflictness. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_11

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  • DOI: https://doi.org/10.1007/978-3-030-29765-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29764-0

  • Online ISBN: 978-3-030-29765-7

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