Skip to main content
Log in

Combining dependent bodies of evidence

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Dempster’s combination rule can only be applied to independent bodies of evidence. One occurrence of dependence between two bodies of evidence is when they result from a common source. This paper proposes an improved method for combining dependent bodies of evidence which takes the significance of the common information sources into consideration. The method is based on the significance weighting operation and the “decombination” operation. A numerical example is illustrated to show the use and effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Cattaneo ME (2011) Belief functions combination without the assumption of independence of the information sources. Int J Approx Reason 52(3):299–315

    Article  MathSciNet  MATH  Google Scholar 

  2. Deng Y, Shi W, Zhu Z, Liu Q (2004) Combining belief functions based on distance of evidence. Decis Support Syst 38(3):489–493

    Article  Google Scholar 

  3. Denœux T (2008) Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artif Intell 172(2):234–264

    Article  MathSciNet  MATH  Google Scholar 

  4. Deng Y (2015) Generalized evidence theory. Appl Intell 43(3):530–543

    Article  Google Scholar 

  5. Destercke S, Dubois D (2011) Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory. Inf Sci 181(18):3925–3945

    Article  MathSciNet  MATH  Google Scholar 

  6. Guralnik V, Mylaraswamy D, Voges H (2006) On handling dependent evidence and multiple faults in knowledge fusion for engine health management. In: Aerospace Conference. IEEE, pp 9–17

  7. Huynh V, Nakamori Y, Ho T, Murai T (2006) Multiple-attribute decision making under uncertainty: the evidential reasoning approach revisited. IEEE Transactions on Systems, Man and Cybernetics. Part A: Syst Hum 36(4):804–822

    Google Scholar 

  8. Liu L, Yager RR (2008) Classic works of the dempster-shafer theory of belief functions: An introduction. In: Classic works of the Dempster-Shafer theory of belief functions. Springer, pp 1–34

  9. Monney PA, Chan M (2007) Modelling dependence in dempster-shafer theory. Int J Uncertain Fuzziness Knowl-Based Syst 15(1):93–114

    Article  MathSciNet  MATH  Google Scholar 

  10. Shafer G (1976) A mathematical theory of evidence, Volume 1. In: A Mathematical Theory of Evidence, Volume 1. Princeton university press, Princeton

    Google Scholar 

  11. Smets P (1992) The concept of distinct evidence. In: Proceedings of the 4th Conf on Information Processing and anagement of Uncertainty in Knowledge-based Systems (IPMU). Palma de Mayorca, pp 789–794

  12. Smets P (1995) The canonical decomposition of a weighted belief. In: IJCAI, vol 95, pp 1896–1901

  13. Smets P (2002) The application of the matrix calculus to belief functions. Int J Approx Reason 31(1):1–30

    Article  MathSciNet  MATH  Google Scholar 

  14. Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66(2):191–234

    Article  MathSciNet  MATH  Google Scholar 

  15. Su X, Mahadevan S, Xu P, Deng Y (2015a) Dependence assessment in Human Reliability Analysis using evidence theory and AHP. Risk Anal 35:1296–1316

    Article  Google Scholar 

  16. Su X, Mahadevan S, Xu P, Deng Y (2015b) Handling of dependence in dempstershafer theory. Int J Intell Syst 30:441–467

    Article  Google Scholar 

  17. Wu Y, Yang J, Liu L et al (1996) On the evidence inference theory. Inf Sci 89(3):245–260

    Article  MathSciNet  MATH  Google Scholar 

  18. Xiao W, Wang Z, Wang Y (2011) Combination rule for dependent evidences. Control Decis 26(5):773–776

    MathSciNet  Google Scholar 

  19. Xu P, Su X, Mahadevan S, Deng Y (2014) A non-parametric method to determine basic probability assignment for classification problems. Appl Intell 41(3):681–693

    Article  Google Scholar 

  20. Yager RR (2009) On the fusion of non-independent belief structures. Int J Gen Syst 38(5):505–531

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was partially supported by National Natural Science Foundation of China, Grant No. 61503237, Grant No. 61174022, Grant No. 51107080, Chongqing Natural Science Foundation (for Distinguished Young Scholars), Grant No. CSCT, 2010BA2003, General Motors R & D at Vanderbilt University (Project No. ND0044200), and Joint PhD Student Scholarship of SJTU, Shanghai Key Laboratory of Power Station Automation Technology (No.13DZ2273800).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaoyan Su.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, X., Mahadevan, S., Han, W. et al. Combining dependent bodies of evidence. Appl Intell 44, 634–644 (2016). https://doi.org/10.1007/s10489-015-0723-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-015-0723-5

Keywords

Navigation