Abstract
Preparing for generalization of results on conflicts of classic belief function to DSm approach, we need normalized plausibility of singletons also in DSmT. To enable this, plausibility of DSm generalized belief functions is analyzed and compared on entire spectrum of DSm models for various types of belief functions; from simple uniform distribution, through general classic belief function, to general generalized belief function in full generality. Both numeric and comparative variability with respect to particular DSm models has been observed and described. This comparative study enables deeper understanding of plausibility in DSm approach and also underlines the sensitivity to selection of particular DSm models.
Figure of elements of DSm domain—DSm hyper-power set—and figures representing particular DSm models (the free DSm model, hybrid DSm models, and Shafer’s model) throughout the text enable better understanding of DSm principles.
Further, a notion of non-conflicting DSm model is introduced and characterized towards the end of the study.
This research is supported by the grant P202/10/1826 of the Grant Agency of the Czech Republic. Partial support by the Institutional Research Plan AV0Z10300504 “Computer Science for the Information Society:Models, Algorithms, Applications” is also acknowledged.
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References
Cholvy, L.: Using Logic to Understand Relations between DSmT and Dempster-Shafer Theory. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS(LNAI), vol. 5590, pp. 264–274. Springer, Heidelberg (2009)
Daniel, M.: A Generalization of the Classic Combination Rules to DSm Hyper-power Sets. Information & Security. An International Journal 20, 50–64 (2006)
Daniel, M.: The DSm Approach as a Special Case of the Dempster-Shafer Theory. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 381–392. Springer, Heidelberg (2007)
Daniel, M.: Contribution of DSm Approach to the Belief Function Theory. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proc. of IPMU 2008, Málaga, pp. 417–424 (2008)
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)
Daniel, M.: Non-conflicting and Conflicting Parts of Belief Functions. In: Coolen, F., de Cooman, G., Fetz, T., Oberguggenberger, M. (eds.) Proceedings of the 7th ISIPTA 2011, pp. 149–158. Studia Universitätsverlag, Innsbruck (2011)
Dezert, J.: Foundations for a New Theory of Plausible and Paradoxical Reasoning. Information and Security, An International Journal 9 (2002)
Shafer, G.: A Mathematical Theory of Evidence. Princeton Univ. Press, New Jersey (1976)
Smarandache, F., Dezert, J.: Advances and Applications of DSmT for Information Fusion. American Research Press, Rehoboth (2004)
Smarandache, F., Dezert, J.: Advances and Applications of DSmT for Information Fusion, vol. 2. American Research Press, Rehoboth (2006)
www.gallup.unm.edu/~smarandache/DSmT.htm (cited, January 28, 2012)
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Daniel, M. (2012). Plausibility in DSmT. In: Denoeux, T., Masson, MH. (eds) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29461-7_21
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DOI: https://doi.org/10.1007/978-3-642-29461-7_21
Publisher Name: Springer, Berlin, Heidelberg
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