Abstract
The α-conjunctions basically represent the set of associative, commutative and linear operators for belief functions with the vacuous belief function as neutral element. Besides, they include as particular case the unnormalized Dempster’s rule. They are thus particularly interesting from a formal standpoint. However, they suffer from a main limitation: they lack a clear interpretation in general. In this paper, an interpretation for these combination rules is proposed, based on a new framework that allows the integration of meta-knowledge on the various forms of lack of truthfulness of the information sources.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)
Dubois, D., Prade, H.: A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. International Journal of General Systems 12(3), 193–226 (1986)
Pichon, F., Denœux, T.: Interpretation and computation of α-junctions for combining belief functions. In: Sixth Int. Symp. on Imprecise Probability: Theories and Applications (ISIPTA 2009), Durham, United Kingdom (July 2009)
Pichon, F., Dubois, D., Denœux, T.: Relevance and truthfulness in information correction and fusion. International Journal of Approximate Reasoning 53(2), 159–175 (2012)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Smets, P.: The combination of evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(5), 447–458 (1990)
Smets, P.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9(1), 1–35 (1993)
Smets, P.: The α-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)
Smets, P.: The application of the matrix calculus to belief functions. International Journal of Approximate Reasoning 31(1-2), 1–30 (2002)
Smets, P., Kennes, R.: The Transferable Belief Model. Artif. Intell. 66, 191–243 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pichon, F. (2012). On the α-Conjunctions for Combining Belief Functions. 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_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-29461-7_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29460-0
Online ISBN: 978-3-642-29461-7
eBook Packages: EngineeringEngineering (R0)