Skip to main content
SpringerLink
Log in

An Improved Approach for Generation of a Basic Probability Assignment in the Evidence Theory Based on Gaussian Distribution

  • Research Article-Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Dempster–Shafer evidence theory (D-S theory) is a commonly used reasoning method for uncertain information. Generating the basic probability assignment (BPA) functions is the first step of applying D-S theory in practical engineering. The quality of generated BPA will have a direct impact on the result of evidence fusion and final decision-making. However, the generation of BPA still owns no fixed model. In response to this situation, a new BPA generation method based on the Gaussian distribution is proposed in this paper. First, the Gaussian distribution is constructed based on the mean and variance value of training sample in the data set. Second, calculate the function value of the test sample on the Gaussian distribution to generate BPA function. Third, data fusion based on Dempster’s combination rule. Finally, decision-making based on information fusion. The feasibility and effectiveness of the proposed method are verified in classification problem by using the UCI data sets.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38(2), 325–339 (1967)

    MathSciNet  MATH  Google Scholar 

  2. Shafer, G.: A mathematical theory of evidence. Princeton Univ. Press,, Princeton, NJ, USA (1976)

  3. Xiao, Fuyuan: A multiple-criteria decision-making method based on d numbers and belief entropy. Int. J. Fuzzy Syst. 21(4), 1144–1153 (2019)

    MathSciNet  Google Scholar 

  4. Chao, Fu; Wenjun, Chang; Min, Xue; Shanlin, Yang: Multiple criteria group decision making with belief distributions and distributed preference relations. Eur. J. Op. Res. 27323–633(2), 623–633 (2019)

    MathSciNet  Google Scholar 

  5. Chao, Fu; Bingbing, Hou; Wenjun, Chang; Nanping, Feng; Shanlin, Yang: Comparison of evidential reasoning algorithm with linear combination in decision making. Int. J. Fuzzy Syst. 22(2), 686–711 (2020)

    Google Scholar 

  6. Liguo, Fei; Yong, Deng; Yong, Hu: Ds-vikor: a new multi-criteria decision-making method for supplier selection. Int. J. Fuzzy Syst. 21(1), 157–175 (2019)

    MathSciNet  Google Scholar 

  7. Khan, Nazmuzzaman; Anwar, Sohel: Paradox elimination in dempster-shafer combination rule with novel entropy function: Application in decision-level multi-sensor fusion. Sensors 19(21), 4810 (2019)

    Google Scholar 

  8. Xiao, Fuyuan: Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inform. Fus. 46, 23–32 (2019)

    Google Scholar 

  9. Seiti, Hamidreza; Hafezalkotob, Ashkan: Developing pessimistic-optimistic risk-based methods for multi-sensor fusion: an interval-valued evidence theory approach. Appl. Soft Comput. 72, 609–623 (2018)

    Google Scholar 

  10. Song, Yafei; Wang, Xiaodan; Zhu, Jingwei; Lei, Lei: Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl. Intell. 48(11), 3950–3962 (2018)

    Google Scholar 

  11. Yafei, Song; Xiaodan, Wang; Wenhua, Wu; Wen, Quan; Wenlong, Huang: Evidence combination based on credibility and non-specificity. Pattern Anal. Appl. 21(1), 167–180 (2018)

    MathSciNet  MATH  Google Scholar 

  12. Jianwei, Wang; Yong, Hu; Fuyuan, Xiao; Xinyang, Deng; Yong, Deng: A novel method to use fuzzy soft sets in decision making based on ambiguity measure and dempster-shafer theory of evidence: an application in medical diagnosis. Artif. Intell. Med. 69, 1–11 (2016)

    Google Scholar 

  13. Xiaobin, Xu; Deqing, Zhang; Bai, Yu; Leilei, Chang; Jianning, Li: Evidence reasoning rule-based classifier with uncertainty quantification. Inform. Sci. 516, 192–204 (2020)

    Google Scholar 

  14. Dongdong, Wu: Tang, Yongchuan: an improved failure mode and effects analysis method based on uncertainty measure in the evidence theory. Qual. Reliab. Eng. Int. 36(5), 1786–1807 (2020)

    Google Scholar 

  15. Xiaoyan, Su; Yong, Deng; Sankaran, Mahadevan; Qilian, Bao: An improved method for risk evaluation in failure modes and effects analysis of aircraft engine rotor blades. Eng. Fail. Anal. 26, 164–174 (2012)

    Google Scholar 

  16. Zhun-Ga, Liu; Quan, Pan; Jean, Dezert; Arnaud, Martin: Combination of classifiers with optimal weight based on evidential reasoning. IEEE Trans. Fuzzy Syst. 26(3), 1217–1230 (2017)

    Google Scholar 

  17. Dongdong, Wu; Zijing, Liu; Yongchuan, Tang: A new classification method based on the negation of a basic probability assignment in the evidence theory. Eng. Appl. Artif. Intell. 96, 103985 (2020)

    Google Scholar 

  18. Liu, Zhun-Ga.; Liu, Yu.; Dezert, Jean.; Cuzzolin, Fabio.: Evidence combination based on credal belief redistribution for pattern classification. IEEE Transactions on Fuzzy Systems, 28(4):618–631, (APR 2020).

  19. Zhou, Kuang; Martin, Arnaud; Pan, Quan; Liu, Zhunga: SELP: semi-supervised evidential label propagation algorithm for graph data clustering. Int. J. Approx. Reason. 92, 139–154 (2018)

    MathSciNet  MATH  Google Scholar 

  20. Zhi-gang, Su; Thierry, Denoeux: BPEC: belief-peaks evidential clustering. IEEE Trans. Fuzzy Syst. 27(1), 111–123 (2018)

    Google Scholar 

  21. Jintao, Meng; Dongmei, Fu; Yongchuan, Tang: Belief-peaks clustering based on fuzzy label propagation. Appl. Intell. 50(4), 1259–1271 (2020)

    Google Scholar 

  22. Kang, Bingyi; Zhang, Pengdan; Gao, Zhenyu; Chhipi-Shrestha, Gyan; Hewage, Kasun; Sadiq, Rehan: Environmental assessment under uncertainty using dempster-shafer theory and z-numbers. J. Amb. Intell. Human. Comput. 11(5), 2041–2060 (2020)

    Google Scholar 

  23. Yang Ying, Xu; Dong-Ling, Yang Jian-Bo; Yu-Wang, Chen: An evidential reasoning-based decision support system for handling customer complaints in mobile telecommunications. Knowl. Based Syst. 162(SI), 202–210 (2018)

    Google Scholar 

  24. Zhang, Xiaoge; Mahadevan, Sankaran; Deng, Xinyang: Reliability analysis with linguistic data: an evidential network approach. Reliab. Eng. Syst. Saf. 162, 111–121 (2017)

    Google Scholar 

  25. Deng, Xinyang; Jiang, Wen; Wang, Zhen: Zero-sum polymatrix games with link uncertainty: a dempster-shafer theory solution. Appl. Math. Comput. 340, 101–112 (2019)

    MathSciNet  MATH  Google Scholar 

  26. Jiankun, Ding; Deqiang, Han; Jean, Dezert; Yi, Yang: A new hierarchical ranking aggregation method. Inform. Sci. 453, 168–185 (2018)

    MathSciNet  Google Scholar 

  27. Wen Sheng Du, Bao Qing Hu: Attribute reduction in ordered decision tables via evidence theory. Inform. Sci. 364, 91–110 (2016)

  28. Ma, Jianbing; Liu, Weiru; Miller, Paul; Zhou, Huiyu: An evidential fusion approach for gender profiling. Inform. Sci. 333, 10–20 (2016)

    Google Scholar 

  29. Shengqun, Chen; Yingming, Wang; Hailiu, Shi; Meijing, Zhang; Yang, Lin: Evidential reasoning with discrete belief structures. Inform. Fus. 41, 91–104 (2018)

    Google Scholar 

  30. Fu-Jun, Zhao; Zhou Zhi-Jie, Hu; Chang-Hua, Chang Lei-Lei; Zhi-Guo, Zhou; Gai-Ling, Li: A new evidential reasoning-based method for online safety assessment of complex systems. IEEE Trans. Syst. Man Cybern. Syst. 48(6), 954–966 (2018)

    Google Scholar 

  31. Xiaobin, Xu; Weng, Xu; Xu Dongling, Xu; Yanzhu, Haiyang, Hu; Jianning, Li: Evidence updating with static and dynamical performance analyses for industrial alarm system design. ISA Trans. 99, 110–122 (2020)

    Google Scholar 

  32. Zadeh, Lotfi A.: Review of a mathematical theory of evidence. Ai Mag. 5(3), 81–83 (1984)

    Google Scholar 

  33. Zadeh, Lotfi A.: A simple view of the dempster-shafer theory of evidence and its implication for the rule of combination. Ai Magazine 7(2), 85–90 (1986)

    Google Scholar 

  34. Deng, Yong: Generalized evidence theory. Appl. Intell. 43(3), 530–543 (2015)

    Google Scholar 

  35. Jing, Ming; Tang, Yongchuan: A new base basic probability assignment approach for conflict data fusion in the evidence theory. Appl. Intell. 51(2), 1056–1068 (2021)

    MathSciNet  Google Scholar 

  36. Yuan-Wei, Du; Ying-Ming, Wang; Man, Qin: New evidential reasoning rule with both weight and reliability for evidence combination. Comput. Ind. Eng. 124, 493–508 (2018)

    Google Scholar 

  37. Xiaoyan, Su; Lusu, Li; Hong, Qian; Sankaran, Mahadevan; Yong, Deng: A new rule to combine dependent bodies of evidence. Soft Comput. 23(20), 9793–9799 (2019)

    MATH  Google Scholar 

  38. Xiaoyan, Su; Sankaran, Mahadevan; Peida, Xu; Yong, Deng: Handling of dependence in dempster-shafer theory. Int. J. Intell. Syst. 30(4), 441–467 (2015)

    Google Scholar 

  39. Xiaoyan, Su; Sankaran, Mahadevan; Wenhua, Han; Yong, Deng: Combining dependent bodies of evidence. Appl. Intell. 44(3), 634–644 (2016)

    Google Scholar 

  40. Yi, Yang; Deqiang, Han; Jean, Dezert: Basic belief assignment approximations using degree of non-redundancy for focal element. Chin. J. Aeronaut. 32(11), 2503–2515 (2019)

    Google Scholar 

  41. Deng, Yong: Uncertainty measure in evidence theory. Sci. China Inform. Sci. 63(11), 1–19 (2020)

    MathSciNet  Google Scholar 

  42. Deng, Yong: Deng entropy. Chaos Solitons Fractals 91, 549–553 (2016)

    MATH  Google Scholar 

  43. Deng, Xinyang; Xiao, Fuyuan; Deng, Yong: An improved distance-based total uncertainty measure in belief function theory. Appl. Intell. 46(4), 898–915 (2017)

    Google Scholar 

  44. Jiroušek, Radim., Shenoy Prakash, P.: A new definition of entropy of belief functions in the dempster–shafer theory. Int. J. Approx. Reason., 92:49–65, (2018)

  45. Jiroušek, Radim.; Shenoy, Prakash P.: On properties of a new decomposable entropy of dempster-shafer belief functions. International Journal of Approximate Reasoning, 119:260–279, (2020).

  46. Peida, Xu; Yong, Deng; Xiaoyan, Su; Sankaran, Mahadevan: A new method to determine basic probability assignment from training data. Knowl. Based Syst. 46, 69–80 (2013)

    Google Scholar 

  47. Wen, Jiang; Yan, Yang; Luo, Yu; Xiyun, Qin: Determining basic probability assignment based on the improved similarity measures of generalized fuzzy numbers. Int. J. Comput. Commun. Control 10(3), 333–347 (2015)

    Google Scholar 

  48. Xinyang, Deng; Qi, Liu; Yong, Deng; Sankaran, Mahadevan: An improved method to construct basic probability assignment based on the confusion matrix for classification problem. Inform. Sci. 340, 250–261 (2016)

    Google Scholar 

  49. Tang Yongchuan, Wu Dongdong, Liu Zijing: A new approach for generation of generalized basic probability assignment in the evidence theory. Pattern Anal. Appl., 1–17, (2021)

  50. Fei, Liguo; Xia, Jun; Feng, Yuqiang; Liu, Luning: A novel method to determine basic probability assignment in dempster-shafer theory and its application in multi-sensor information fusion. Int. J. Distrib. Sens. Netw. 15(7), 1550147719865876 (2019)

    Google Scholar 

  51. Dutta, Palash: Uncertainty modeling in risk assessment based on dempster-shafer theory of evidence with generalized fuzzy focal elements. Fuzzy Inform. Eng. 7(1), 15–30 (2015)

  52. Dutta, Palash: Dempster shafer structure-fuzzy number based uncertainty modeling in human health risk assessment. Int. J. Fuzzy Syst. Appl. Archive 5(2), 96–117 (2016)

    Google Scholar 

  53. Ma, Tianshuo; Xiao, Fuyuan: An improved method to transform triangular fuzzy number into basic belief assignment in evidence theory. IEEE Access 7, 25308–25322 (2019)

    Google Scholar 

  54. Gao, Xiaozhuan; Deng, Yong: The negation of basic probability assignment. IEEE Access 7, 107006–107014 (2019)

    Google Scholar 

  55. Ronald Aylmer Fisher: The use of multiple measurements in taxonomic problems. Ann. Human Genet. 7(2), 179–188 (1936)

  56. Murphy, Catherine K.: Combining belief functions when evidence conflicts. Decis. Supp. Syst. Archive 29, 1–9 (2000)

    Google Scholar 

  57. Xiao, Fuyuan: An improved method for combining conflicting evidences based on the similarity measure and belief function entropy. Int. J. Fuzzy Syst. 20(4), 1256–1266 (2018)

    MathSciNet  Google Scholar 

  58. Zhang, Weiquan; Deng, Yong: Combining conflicting evidence using the dematel method. Soft Comput. 23, 8207–8216 (2019)

    Google Scholar 

  59. Yong, Deng; WenKang, Shi; ZhenFu, Zhu; Qi, Liu: Combining belief functions based on distance of evidence. Decis. Supp. Syst. Archive 38, 489–493 (2004)

    Google Scholar 

  60. Liu, Fan., Deng, Yong.: Determine the number of unknown targets in open world based on elbow method. IEEE Trans Fuzzy Syst. 1–1, (2020)

Download references

Author information

Authors and Affiliations

  1. School of Big Data and Software Engineering, Chongqing University, Chongqing, 401331, China

    Shuning Wang & Yongchuan Tang

Authors
  1. Shuning Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongchuan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongchuan Tang.

Additional information

This work was supported in part by the National Key Research and Development Project of China (Grant No. 2020YFB1711900)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Tang, Y. An Improved Approach for Generation of a Basic Probability Assignment in the Evidence Theory Based on Gaussian Distribution. Arab J Sci Eng 47, 1595–1607 (2022). https://doi.org/10.1007/s13369-021-06011-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-06011-w

Keywords

Search

Navigation