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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References
Burger, T.: Geometric views on conflicting mass functions: from distances to angles. Int. J. Approximate Reasoning 70, 36–50 (2016)
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)
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
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
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)
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
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
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)
Daniel, M., Kratochvíl, V.: On hidden conflict of belief functions. In: Proceedings of EUSFLAT 2019 (2019, in print)
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
Destercke, S., Burger, T.: Toward an axiomatic definition of conflict between belief functions. IEEE Trans. Cybern. 43(2), 585–596 (2013)
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
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)
Liu, W.: Analyzing the degree of conflict among belief functions. Artif. Intell. 170(11), 909–924 (2006)
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
R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2016). https://www.R-project.org/
RStudio Team: RStudio: Integrated Development Environment for R. RStudio Inc., Boston (2015). http://www.rstudio.com/
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)
Shafer, G.: A Mathematical Theory of Evidence, vol. 1. Princeton University Press, Princeton (1976)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approximate Reasoning 38(2), 133–147 (2005)
Smets, P.: Analyzing the combination of conflicting belief functions. Inf. Fusion 8(4), 387–412 (2007)
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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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