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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 219))

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Abstract

This article gives an algorithm for the exact implementation of Dempster’s rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of hierarchical evidence.

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References

  • Barnett, J.A., Computational methods for a mathematical theory of evidence, in: Proceedings IJCAI-81, Vancouver, BC (1981) 868–875.

    Google Scholar 

  • Garvey, T.D., Lowrance, J.D. and Fischler, M.A., An inference technique for integrating knowledge from disparate sources, in: Proceedings IJCAI-81, Vancouver, BC (1981) 319–325.

    Google Scholar 

  • Gordon, J. and Shortliffe, E.H., The Dempster–Shafer theory of evidence, in: B.G. Buchanan and E.H Shortliffe (Eds.), Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project (Addison-Wesley, Reading, MA, 1985) 272–292.

    Google Scholar 

  • Gordon, J. and Shortliffe, E.H., A method for managing evidential reasoning in a hierarchical hypothesis space, Artificial Intelligence 26 (1985) 323–357.

    Article  MathSciNet  MATH  Google Scholar 

  • Kong, A., Multivariate belief functions and graphical models, Doctoral Dissertation, Department of Statistics, Harvard University, Cambridge, MA, 1986.

    Google Scholar 

  • Mellouli, K., Shafer, G. and Shenoy, P., Qualitative Markov networks, in: International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris (1986) 31–35.

    Google Scholar 

  • Pearl, J., On evidential reasoning in a hierarchy of hypotheses, Artificial Intelligence 28 (1986) 9–15.

    Article  Google Scholar 

  • Pearl, J., Fusion, propagation, and structuring in belief networks, Artificial Intelligence 29 (1986) 241–288.

    Article  MATH  MathSciNet  Google Scholar 

  • Shafer, G., A Mathematical Theory of Evidence (Princeton University Press, Princeton, NJ, 1976.

    MATH  Google Scholar 

  • Shafer, G., Belief functions and possibility measures, in: J.C. Bizdek (Ed.), The Analysis of Fuzzy Information 2 (CRC Press, 1987).

    Google Scholar 

  • Shafer, G., Probability judgment in artificial intelligence and expert systems, Stat. Sci. 2 (1987) 3–16.

    Article  MATH  MathSciNet  Google Scholar 

  • Shafer, G., Hierarchical evidence, in: Proceedings Second Conference on Artificial Intelligence Applications, Miami, FL (1985) 16–21.

    Google Scholar 

  • Shafer, G., Shenoy, P. and Mellouli, K., Propagating belief functions in qualitative Markov trees, Working Paper No. 190, School of Business, University of Kansas, Lawrence, KS, 1987.

    Google Scholar 

  • Shenoy, P. and Shafer, G., Propagating belief functions with local computations, IEEE Expert 1(3) (1986) 43–52.

    Article  Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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Shafer, G., Logan, R. (2008). Implementing Dempster’s Rule for Hierarchical Evidence. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_18

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  • DOI: https://doi.org/10.1007/978-3-540-44792-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25381-5

  • Online ISBN: 978-3-540-44792-4

  • eBook Packages: EngineeringEngineering (R0)

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