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Brazilian Symposium on Artificial Intelligence

SBIA 1995: Advances in Artificial Intelligence pp 39–48Cite as

Sensitivity of combination schemes under conflicting conditions and a new method

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 991))

Abstract

In the theory of evidential reasoning, Dempster's rule is used for combining belief functions based on independent evidences. There has been a lot of debate over the counter-intuitive nature of results obtained by this rule [4, 8, 14, 15]. Dubois and Prade [1, 3] have shown that Dempster's rule is not robust and is sensitive to inaccurate estimates of uncertainty values. Many authors have suggested modifications which overcome this drawback.

In this paper, we first bring out the limitation of the combination rule introduced by Zhang [16]. Subsequently, we focus our study on two other rules. The first one was proposed by Dubois and Prade [2, 3] and is known as Disjunctive rule of combination. Incidentally, this rule also appeared in the Hau and Kashyap's work [5]. The other combination rule was due to Yager [13]. Even though these rules are robust, we show that in some cases these rules treat evidences asymmetrically and give counterintuitive results. We then propose a combination rule which doesn't have these drawback. An intuitive justification for this rule is also provided.

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References

  1. D. Dubois and H. Prade. Combination and Propagation of Uncertainty with Belief Functions: A Reexamination. Proc. 9th IJCAI, pages 111–113, Los Angeles, 1985.

    Google Scholar 

  2. D. Dubois and H. Prade. A Set-theoretic View of Belief Functions. International Journal of General Systems, 12:193–226, 1986.

    Google Scholar 

  3. D. Dubois and H. Prade. Representation and Combination of Uncertainty with Belief Functions and Possibility Measures. Computational Intelligence, 4:244–264, 1988.

    Google Scholar 

  4. J. Halpern and R. Fagin. Two Views of Belief: Belief as Generalized Probability and Belief as Evidence. Artificial Intelligence, 54:275–317, 1992.

    Article  Google Scholar 

  5. H. Hau and R. Kashyap. Belief Combination and Propagation in a Lattice Structured Inference Network. IEEE Transactions on Systems, Man and Cybernetics, 20(1):45–57, 1990.

    Google Scholar 

  6. M. McLeish. A Study of Probabilities and Belief Functions under Conflicting Evidence. In B. Bouchon, R. Yager, and L. Zadeh, editors, Uncertainty in Knowledge Bases, Lecture Notes in Computer Science, pages 41–49, France, 1990. Springer-Verlag.

    Google Scholar 

  7. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, New Jersy, 1976.

    Google Scholar 

  8. G. Shafer. Analysis of Fuzzy Information, volume 1, chapter Belief Functions and Possibility Measures, pages 51–83. CRC Press, 1987. J. Bezdek Editor.

    Google Scholar 

  9. G. Shafer. Readings in Uncertain Reasoning, chapter Belief Functions, pages 473–481. Morgan Kauffman, 1990. G. Shafer and J. Pearl Eds.

    Google Scholar 

  10. Shi ShengLi, M.E.C Hull, and D.A. Bell. A New Rule for Updating Evidence. In Z. Ras and M. Zemankova, editors, Methodology for Intelligent Systems, number 869 in Lecture Notes in Artificial Intelligence, pages 95–104, Berlin, 1994. Springer-Verlag.

    Google Scholar 

  11. P. Smets. Non-standard Logics for Automated Reasoning, chapter Belief Functions, pages 253–286. Academic Press, 1988. D. Dubois and H. Prade Eds.

    Google Scholar 

  12. P. Smets. The Combination of Evidence in Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5):447–458, 1990.

    Article  Google Scholar 

  13. R. Yager. On the Dempster-Shafer Framework and New Combination Rules. International Journal of Man-Machine Studies, 41:93–137, 1987.

    Google Scholar 

  14. L. Zadeh. Review of Shafer's A Mathematical Theory of Evidence. AI Magazine, 5(3):81–83, 1984.

    Google Scholar 

  15. L. Zadeh. A Simple View of the Dempster-Shafer Theory of Evidence and Its Implication for the Rule of Combination. AI Magazine, 7:85–90, 1986.

    Google Scholar 

  16. L. Zhang. Advances in the Dempster-Shafer Theory of Evidence, chapter Representation, Independence and Combination of Evidence in the Dempster-Shafer Theory, pages 51–69. Wiley Professional Computing. John Wiley & Sons, New York, 1994. R. Yager and M. Fedrizzi and J. Kacprzyk Eds.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Electrical Engineering Department, Indian Institute of Technology, 400 076, Powai, Bombay, India

    A. V. Joshi, S. C. Sahasrabudhe & K. Shankar

Authors
  1. A. V. Joshi
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  2. S. C. Sahasrabudhe
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  3. K. Shankar
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Editor information

Jacques Wainer Ariadne Carvalho

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© 1995 Springer-Verlag Berlin Heidelberg

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Joshi, A.V., Sahasrabudhe, S.C., Shankar, K. (1995). Sensitivity of combination schemes under conflicting conditions and a new method. In: Wainer, J., Carvalho, A. (eds) Advances in Artificial Intelligence. SBIA 1995. Lecture Notes in Computer Science, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034797

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  • DOI: https://doi.org/10.1007/BFb0034797

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60436-5

  • Online ISBN: 978-3-540-47467-8

  • eBook Packages: Springer Book Archive

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