Pattern Analysis and Applications

, Volume 21, Issue 1, pp 167–180 | Cite as

Evidence combination based on credibility and non-specificity

  • Yafei Song
  • Xiaodan Wang
  • Wenhua Wu
  • Wen Quan
  • Wenlong Huang
Theoretical Advances


This paper addresses the combination of unreliable evidence sources which provide uncertain information in the form of basic probability assignment (BPA) functions. We proposed a novel evidence combination rule based on credibility and non-specificity of belief functions. Following a review of all existing non-specificity measures in evidence theory, a non-specificity measure for evidence theory is discussed. It is claimed that the non-specificity degree of a BPA is related to its ability of pointing to one and only one element. Based on the difference between the largest belief grades and other belief grades, a non-specificity measure is defined. Properties of the proposed non-specificity measure are put forward and proved mathematically. Illustrative examples are employed to show the properties of non-specificity measure. After providing a procedure for the evaluation of evidence credibility, we propose a novel evidence combination rule. Numerical example and application in target identification are applied to demonstrate the performance of our proposed evidence combination rule.


Evidence theory Belief function Non-specificity degree Credibility degree 


  1. 1.
    Dempster AP (1967) Upper and lower probabilities induced by a multiple valued mapping. Ann Math Stat 38(2):325–339CrossRefMATHGoogle Scholar
  2. 2.
    Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonMATHGoogle Scholar
  3. 3.
    Liu Z-G, Pan Q, Dezert J, Martin A (2016) Adaptive imputation of missing values for incomplete pattern recognition. Pattern Recogn 52(1):85–95CrossRefGoogle Scholar
  4. 4.
    Smarandache F, Dezert J (2009) Applications and advances of DSmT for information fusion, vol 3. American Research Press, Rehoboth, pp 4–32MATHGoogle Scholar
  5. 5.
    Lefevre E, Colot O, Vannoorenberghe P (2002) Belief functions combination and conflict management. Inf Fusion 3(2):149–162CrossRefGoogle Scholar
  6. 6.
    Smets P (2000) Data fusion in the transferable belief model. In: Proceedings of the 3rd international conference on information fusion, Paris, France, pp PS21–PS33Google Scholar
  7. 7.
    Florea MC, Jousselme A-L, Bosse E (2009) Robust combination rules for evidence theory. Inf Fusion 10(2):183–197CrossRefGoogle Scholar
  8. 8.
    Liu Z-G, Pan Q, Dezert J (2014) A belief classification rule for imprecise data. Appl Intell 40(2):214–228CrossRefGoogle Scholar
  9. 9.
    Yager RR (1987) On the Dempster–Shafer framework and new combination rules. Inf Sci 41(2):93–137MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Haenni R (2005) Shedding new light on Zadeh’s criticism of Dempster’s rule of combination. In: Proceedings of the eighth international conference on information fusion, Philadelphia, USA. IEEE, Piscataway, pp 879–884Google Scholar
  11. 11.
    Murphy CK (2000) Combining belief functions when evidence conflicts. Decis Support Syst 29(1):1–9MathSciNetCrossRefGoogle Scholar
  12. 12.
    Deng Y, Shi WK, Zhu ZF, Liu Q (2004) Combining belief functions based on distance of evidence. Decis Support Syst 38(3):489–493CrossRefGoogle Scholar
  13. 13.
    Klein J, Colot O (2010) Automatic discounting rate computation using a dissent criterion. In: Proceedings of the workshop on the theory of belief functions, Brest, France, pp 1–6Google Scholar
  14. 14.
    Yang Y, Han D, Han C (2013) Discounted combination of unreliable evidence using degree of disagreement. Int J Approx Reason 54(8):1197–1216CrossRefMATHGoogle Scholar
  15. 15.
    Elouedi Z, Mellouli K, Smets P (2004) Assessing sensor reliability for multisensor data fusion within the transferable belief model. IEEE Trans Syst Man Cybern B Cybern 34(4):782–787CrossRefMATHGoogle Scholar
  16. 16.
    Guo H, Shi W, Deng Y (2006) Evaluating sensor reliability in classification problems based on evidence theory. IEEE Trans Syst Man Cybern B Cybern 36(5):970–981CrossRefGoogle Scholar
  17. 17.
    Schubert J (2011) Conflict management in Dempster–Shafer theory using the degree of falsity. Int J Approx Reason 52(3):449–460MathSciNetCrossRefGoogle Scholar
  18. 18.
    Jousselme A-L, Grenier D, Bosse E (2001) A new distance between two bodies of evidence. Inf Fusion 2(2):91–101CrossRefGoogle Scholar
  19. 19.
    Liu Z-G, Dezert J, Pan Q, Mercier G (2011) Combination of sources of evidence with different discounting factors based on a new dissimilarity measure. Decis Support Syst 52(1):133–141CrossRefGoogle Scholar
  20. 20.
    Guo K, Li W (2011) Combination rule of D–S evidence theory based on the strategy of cross merging between evidences. Expert Syst Appl 38(10):13360–13366CrossRefGoogle Scholar
  21. 21.
    Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66(2):191–243MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall, Upper Saddle RiverMATHGoogle Scholar
  23. 23.
    Hartley RVL (1928) Transmission of information. Bell Syst Technol J 7:535–563CrossRefGoogle Scholar
  24. 24.
    Shannon CE (1948) A mathematical theory of communication. Bell Syst Technol J 27:623–656MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Jousselme A-L, Liu C, Grenier D, Bosse E (2006) Measuring ambiguity in the evidence theory. IEEE Trans Syst Man Cybern A Syst Hum 36(5):890–903CrossRefGoogle Scholar
  26. 26.
    Dubois D, Prade H (1985) A note on measures of specificity for fuzzy sets. Int J Gen Syst 10(4):279–283MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Yager RR (1982) Measuring tranquility and anxiety in decision making: an application of fuzzy sets. Int J Gen Syst 8:139–146MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Yager RR (1981) Measurement of properties of fuzzy sets and possibility distributions. In: Proceedings of third international seminar on fuzzy sets, Linz, pp 211–222Google Scholar
  29. 29.
    Yager RR (1983) Entropy and specificity in a mathematical theory of evidence. Int J Gen Syst 9(4):249–260MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Yager RR (2009) Some aspects of intuitionistic fuzzy sets. Fuzzy Optim Decis Mak 8(1):67–90MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Song Y, Wang X, Lei L, Xue A (2014) Combination of interval-valued belief structures based on intuitionistic fuzzy set. Knowl Based Syst 67(9):61–70CrossRefGoogle Scholar
  32. 32.
    Song Y, Wang X, Lei L, Xue A (2014) Measurement of evidence conflict based on correlation coefficient. J Commun 35(5):95–100Google Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Yafei Song
    • 1
    • 2
  • Xiaodan Wang
    • 2
  • Wenhua Wu
    • 3
  • Wen Quan
    • 2
  • Wenlong Huang
    • 2
  1. 1.Xijing UniversityXi’anPeople’s Republic of China
  2. 2.Air Force Engineering UniversityXi’anPeople’s Republic of China
  3. 3.Xi’an Communications InstituteXi’anPeople’s Republic of China

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