Assessing multiple beliefs according to one body of evidence — Why it may be necessary, and how we might do it correctly

  • Yen-Teh Hsia
1. Mathematical Theory Of Evidence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)


Dempster's rule of combination, the main inference mechanism of the Dempster-Shafer theory of belief functions [Shafer 76; Smets 88], requires that the belief functions to be combined must be "independent". This independence assumption is usually understood to be composed of two parts: (1) the uniqueness assumption, which states that each belief function to be combined is based on a unique body of evidence, and (2) the evidential independence (or distinctness) assumption, which states that we must be able to argue about the independence of all these different bodies of evidence. In this paper, we suggest that the uniqueness assumption is not necessary, and that it should be alright if we can come up with "independent specifications" of beliefs.


Belief function Dempster's rule of combination the uniqueness assumption the distinctness assumption specification independence 


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  1. Dubois, D. and Prade, H. (1986). The principle of minimum specificity as a basis for evidential reasoning. In Uncertainty in Knowledge-Based Systems (Bouchon and Yager eds.), Springer-Verlag, Berlin, 75–84.Google Scholar
  2. Hsia, Y.-T. and Shenoy, P. P. (1989). An evidential language for expert systems. Proceedings of the 4th International Symposium on Methodology for Intelligent Systems, Charlotte, N.C., 9–16.Google Scholar
  3. Kong, A. (1986). Multivariate belief functions and graphical models. Doctoral dissertation, Department of Statistics, Harvard University.Google Scholar
  4. Pearl, J. (1986). Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29, 241–288.CrossRefMathSciNetGoogle Scholar
  5. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann Publishers, Inc., San Mateo, California.Google Scholar
  6. Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.Google Scholar
  7. Shafer, G., Shenoy, P., and Mellouli, K. (1987). "Propagating belief functions in Qualitative Markov Trees", International Journal of Approximate Reasoning, 1, 4, 349–400.CrossRefGoogle Scholar
  8. Smets, P. (1978). Un modèle mathématico-statistique simulant le processus du diagnostic médical. Doctoral dissertation, Université Libre de Bruxelles, Bruxelles.Google Scholar
  9. Smets, P. (1988). Belief functions. In Non-Standard Logics for Automated Reasoning (P. Smets, E. H. Mamdani, D. Dubois and H. Prade eds.). Academic Press, London.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Yen-Teh Hsia
    • 1
  1. 1.IRIDIA, Université Libre de BruxellesBrusselsBelgium

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