Alternative Methods for Combining Probability Boxes

Oleg Uzhga-Rebrov, Galina Kuleshova


Probability boxes (p-boxes) are used as a tool for modeling uncertainty regarding probability distributions in the sets of relevant elements (random events, values of the random variable etc.). To combine information produced by two or more p-boxes, Dempster’s rule for belief combination is commonly used. However, there are plenty of other rules for belief combination developed within the theory of evidence. The purpose of this paper is to present and analyze some widespread rules of that kind as well as examine their potentialities regarding combining the information provided by probability boxes.


Basic probability assignments; belief combination rules; p-boxes; theory of evidence

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K. Sentz and S. Ferson, “Combination of evidence in Dempster-Shafer theory,” Sandia National Laboratories, vol. 4015, 2002.

S. Ferson, V. Kreinovich, L. Ginzburg, D. Myers and U. Sentz, “Constructing Probability Boxes and Dempster-Shafer Structures”, SAND Report, Sandia National Laboratories, Albuquerque, New Mexico, California, 2003.

V. Montgomery, “New Statistical Methods in Risk Assessment by Probability Bounds”, Ph. D. thesis, Durham University, UK, 2009.

G. Shafer, A mathematical theory of evidence, Princeton University Press, 1976.

A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping”, Annals of Mathematical Statistics, 38, pp. 325– 339, 1967.

W. Liu and J. Hong, “Re-investigating Dempster’s Idea on Evidence Combination,” Knowledge and Information Systems, vol. 2, no. 2. [Online]. Available:, 2000. [Accessed May 6, 2014].

D. Dubois and H. Prade, “Focusing versus updating in belief function theory,” Advances in the Dempster-Shafer Theory of Evidence. R. R. Yager, J. Kacprzyk, M. Fidrizzi, Eds., New York, John Wiley&Sons, Inc., pp. 71–95, 1994.

О. I. Uzhga-Rebrov, Upravlenije neopredelennostjami. Chastj 3. Sovremennije neverojatnostnije metodi. Rēzekne, RA Izdevniecība, 2010. (In Russian).

О. I. Uzhga-Rebrov, Upravlenije neopredelennostjami. Chastj 4. Kombinirovanije neopredelennostej, Rēzekne, RA Izdevniecība, 2014. (In Russian).

R. Yager, “On the Dempster-Shafer Framework and New Combination Rules”, Information Sciences, vol. 41, no. 2, pp.93–137, 1987.

H. Zhang, R. L. Mullen and R. L. Muhanna, “Finite Element Structural Analysis Using Imprecise Probabilities Based on P-Box Representation,” 4th International Workshop on Reliable Engineering Computing, REC 2010, Singapore, pp. 211–225, 2010.

L. Zhang, “Representation, independence and combination of evidence in the Dempster-Shafer Theory of Evidence”, Advances into the Dempster-Shafer Theory of Evidence. R. R. Yager, J. Kacprzyk, M. Fedrizzi, Eds, New York, John Wiley&Sons, Inc., pp. 51–69, 1994.


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