Skip to main content
SpringerLink
Log in

A new approach for generation of generalized basic probability assignment in the evidence theory

  • Theoretical advances
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

The process of information fusion needs to deal with a large number of uncertain information with multi-source, heterogeneity, inaccuracy, unreliability, and incompleteness. In practical engineering applications, Dempster–Shafer evidence theory is widely used in multi-source information fusion owing to its effectiveness in data fusion. Information sources have an important impact on multi-source information fusion in an environment with the characteristics of complex, unstable, uncertain, and incomplete. To address multi-source information fusion problem, this paper considers the situation of uncertain information modeling from the closed-world to the open-world assumption and studies the generation of basic probability assignment with incomplete information. A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy number representation model. Then, by calculating the length of the intersection points between the sample and the triangular fuzzy number model, a GBPA set with an assignment for the empty set can be determined. The proposed method can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing. Finally, a series of comprehensive experiments basing on the UCI data sets is used to verify the rationality and superiority of the proposed method.

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. Hu Z, Nie F, Wang R, Li X (2020) Multi-view spectral clustering via integrating nonnegative embedding and spectral embedding. Inf Fusion 55:251–259

    Article  Google Scholar 

  2. Wei W, Liang J (2019) Information fusion in rough set theory: an overview. Inf Fusion 48:107–118

    Article  Google Scholar 

  3. Zhang L, Wu X, Zhu H, AbouRizk SM (2017) Perceiving safety risk of buildings adjacent to tunneling excavation: an information fusion approach. Autom Constr 73:88–101

    Article  Google Scholar 

  4. Zhou D, Al-Durra A, Gao F, Ravey A, Matraji I, Simões MG (2017) Online energy management strategy of fuel cell hybrid electric vehicles based on data fusion approach. J Power Sources 366:278–291

    Article  Google Scholar 

  5. He Z, Jiang W (2018) An evidential dynamical model to predict the interference effect of categorization on decision making results. Knowl Based Syst 150:139–149

    Article  Google Scholar 

  6. Xu Z, Na Z (2016) Information fusion for intuitionistic fuzzy decision making: an overview. Inf Fusion 28:10–23

    Article  Google Scholar 

  7. Banerjee TP, Das S (2012) Multi-sensor data fusion using support vector machine for motor fault detection. Inf Sci 217:96–107

    Article  Google Scholar 

  8. Hui KH, Lim MH, Leong MS, Al-Obaidi SM (2017) Dempster-Shafer evidence theory for multi-bearing faults diagnosis. Eng Appl Artif Intell 57:160–170

    Article  Google Scholar 

  9. Lin Y, Li Y, Yin X, Dou Z (2018) Multisensor fault diagnosis modeling based on the evidence theory. IEEE Trans Reliab 67(2):513–521

    Article  Google Scholar 

  10. Song Y, Wang X, Zhu J, Lei L (2018) Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl Intell 48(11):3950–3962

    Article  Google Scholar 

  11. Chemweno P, Pintelon L, Muchiri PN, Van Horenbeek A (2018) Risk assessment methodologies in maintenance decision making: a review of dependability modelling approaches. Reliab Eng Syst Saf 173:64–77

    Article  Google Scholar 

  12. Dutta P (2017) Modeling of variability and uncertainty in human health risk assessment. MethodsX 4:76–85

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Chen L, Deng Y (2018) A new failure mode and effects analysis model using Dempster-Shafer evidence theory and grey relational projection method. Eng Appl Artif Intell 76:13–20

    Article  Google Scholar 

  15. Liu Z-G, Pan Q, Dezert J, Martin A (2017) Combination of classifiers with optimal weight based on evidential reasoning. IEEE Trans Fuzzy Syst 26(3):1217–1230

    Article  Google Scholar 

  16. Habtie AB, Abraham A, Midekso D (2015) Comparing measurement and state vector data fusion algorithms for mobile phone tracking using a-gps and u-tdoa measurements. In: International conference on hybrid artificial intelligence systems. Springer, pp 592–604

  17. Liu Z, Pan Q, Dezert J, Han J-W, He Y (2017) Classifier fusion with contextual reliability evaluation. IEEE Trans Cybern 48(5):1605–1618

    Article  Google Scholar 

  18. Ebrahimnejad A, Verdegay JL (2018) Fuzzy set theory. In: Fuzzy sets-based methods and techniques for modern analytics. Springer, pp 1–27

  19. Frikha A, Moalla H (2015) Analytic hierarchy process for multi-sensor data fusion based on belief function theory. Eur J Oper Res 241(1):133–147

    Article  MathSciNet  MATH  Google Scholar 

  20. Deng X, Xiao F, Deng Y (2017) An improved distance-based total uncertainty measure in belief function theory. Appl Intell 46(4):898–915

    Article  Google Scholar 

  21. Gnedenko BV (2018) Theory of probability. Routledge, London

    Book  Google Scholar 

  22. Tuckwell HC (2018) Elementary applications of probability theory. Routledge, London

    MATH  Google Scholar 

  23. Kang B, Chhipi-Shrestha G, Deng Y, Hewage K, Sadiq R (2018) Stable strategies analysis based on the utility of z-number in the evolutionary games. Appl Math Comput 324:202–217

    MathSciNet  MATH  Google Scholar 

  24. Zadeh LA (2011) A note on z-numbers. Inf Sci 181(14):2923–2932

    Article  MATH  Google Scholar 

  25. Li X, Chen X (2018) D-intuitionistic hesitant fuzzy sets and their application in multiple attribute decision making. Cogn Comput 10(3):496–505

    Article  Google Scholar 

  26. Xiao F (2018) A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on d numbers. Eng Appl Artif Intell 71:216–225

    Article  Google Scholar 

  27. Xu Z, Wang H (2017) On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Inf Fusion 34:43–48

    Article  Google Scholar 

  28. Dubois D, Liu W, Ma J, Prade H (2016) The basic principles of uncertain information fusion. an organised review of merging rules in different representation frameworks. Inf Fusion 32:12–39

    Article  Google Scholar 

  29. Bernardo JM, Smith AFM (2009) Bayesian theory, vol 405. Wiley, New York

    Google Scholar 

  30. Dempster AP (1967) Upper and lower probabilities induced by a multi-valued mapping. Ann Math Stat 38(2):325–339

    Article  MATH  Google Scholar 

  31. Shafer G (1976) A mathematical theory of evidence, vol 42. Princeton University Press, Princeton

    Book  MATH  Google Scholar 

  32. Jiao Z, Gong H, Wang Y (2016) A ds evidence theory-based relay protection system hidden failures detection method in smart grid. IEEE Trans Smart Grid 9(3):2118–2126

    Article  Google Scholar 

  33. Liu Y-T, Pal NR, Marathe AR, Lin C-T (2017) Weighted fuzzy Dempster-Shafer framework for multimodal information integration. IEEE Trans Fuzzy Syst 26(1):338–352

    Article  Google Scholar 

  34. Su Z, Thierry D (2018) Bpec: Belief-peaks evidential clustering. IEEE Trans Fuzzy Syst 27(1):111–123

    Article  Google Scholar 

  35. Meng J, Fu D, Tang Y (2020) Belief-peaks clustering based on fuzzy label propagation. Appl Intell 50:1259–1271

    Article  Google Scholar 

  36. Pan Y, Zhang L, Li ZW, Ding L (2019) Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D-S evidence theory. IEEE Trans Fuzzy Syst 28(9):2063–2077

    Article  Google Scholar 

  37. Luo J, Shi L, Ni Y (2017) Uncertain power flow analysis based on evidence theory and affine arithmetic. IEEE Trans Power Syst 33(1):1113–1115

    Article  Google Scholar 

  38. Xie C, Bai J, Zhu W, Lu G, Wang H (2017) Lightning risk assessment of transmission lines based on D–S theory of evidence and entropy-weighted grey correlation analysis. In: 2017 IEEE conference on energy internet and energy system integration (EI2). IEEE, pp 1–6

  39. Huang ZL, Jiang C, Zhang Z, Zhang W, Yang TG (2019) Evidence-theory-based reliability design optimization with parametric correlations. Struct Multidiscip Optim 60(2):565–580

    Article  MathSciNet  Google Scholar 

  40. Fu C, Xu D-L, Min X (2018) Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions. Knowl Based Syst 143:127–141

    Article  Google Scholar 

  41. Liu J, Li Q, Yu WC, Wang YX (2018) A fast fault diagnosis method of the PEMFC system based on extreme learning machine and Dempster–Shafer evidence theory. IEEE Trans Transport Electr 5(1):271–284

    Article  Google Scholar 

  42. Fei L, Deng Y (2019) A new divergence measure for basic probability assignment and its applications in extremely uncertain environments. Int J Intell Syst 34(4):584–600

    Article  Google Scholar 

  43. de Oliveira Silva LG, de Almeida-Filho AT (2016) A multicriteria approach for analysis of conflicts in evidence theory. Inf Sci 346:275–285

    Article  MATH  Google Scholar 

  44. Yager RR (1987) On the Dempster–Shafer framework and new combination rules. Inf Sci 41(2):93–137

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  47. Su X, Sankaran M, Xu P, Yong D (2015) Handling of dependence in Dempster–Shafer theory. Int J Intell Syst 30(4):441–467

    Article  Google Scholar 

  48. Zhang W, Deng Y (2019) Combining conflicting evidence using the DEMATEL method. Soft Comput 23(17):8207–8216

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  50. Song Y, Wang X, Wu W, Wen Q, Huang W (2018) Evidence combination based on credibility and non-specificity. Pattern Anal Appl 21(1):167–180

    Article  MathSciNet  MATH  Google Scholar 

  51. Xiao F (2019) Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf Fusion 46:23–32

    Article  Google Scholar 

  52. Xu P, Yong D, Su X, Sankaran M (2013) A new method to determine basic probability assignment from training data. Knowl Based Syst 46:69–80

    Article  Google Scholar 

  53. Zhang Z, Han D, Dezert J, Yang Y (2017) Determination of basic belief assignment using fuzzy numbers. In: 2017 20th international conference on information fusion (fusion). IEEE, pp 1–6

  54. Yin L, Deng X, Deng Y (2018) The negation of a basic probability assignment. IEEE Trans Fuzzy Syst 27(1):135–143

    Article  Google Scholar 

  55. Jingfei Zhang, Yong Deng (2017) A method to determine basic probability assignment in the open world and its application in data fusion and classification. Appl Intell 46(4):934–951

    Article  Google Scholar 

  56. Wen J, Hu W (2018) An improved soft likelihood function for Dempster-Shafer belief structures. Int J Intell Syst 33(6):1264–1282

    Article  Google Scholar 

  57. Deng Y, Han D (2011) Methods to determine generalized basic probability assignment in generalized evidence theory. J Xi’an JiaoTong Univ 45(2):34–38

    Google Scholar 

  58. Wen J, Jun Z (2017) A modified combination rule in generalized evidence theory. Appl Intell 46(3):630–640

    Article  Google Scholar 

  59. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  60. Deng X, Jiang W (2020) On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation. Inf Sci 516:346–352

    Article  MathSciNet  MATH  Google Scholar 

  61. Luo Z, Deng Y (2019) A matrix method of basic belief assignment’s negation in Dempster–Shafer theory. IEEE Trans Fuzzy Syst 28(9):2270–2276

    Article  Google Scholar 

  62. Liu F, Deng Y (2020) Determine the number of unknown targets in open world based on elbow method. IEEE Trans Fuzzy Syst

  63. Nesa N, Banerjee I (2017) Iot-based sensor data fusion for occupancy sensing using Dempster-Shafer evidence theory for smart buildings. IEEE Internet Things J 4(5):1563–1570

    Article  Google Scholar 

  64. Wu D, Liu Z, Tang Y (2020) A new classification method based on the negation of a basic probability assignment in the evidence theory. Eng Appl Artif Intell 96:103985

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  66. Zhang H, Liu G, Chow TWS, Liu W (2011) Textual and visual content-based anti-phishing: a Bayesian approach. IEEE Trans Neural Netw 22(10):1532–1546

    Article  Google Scholar 

  67. Chen F-C, Jahanshahi MR, Wu R-T, Chris J (2017) A texture-based video processing methodology using Bayesian data fusion for autonomous crack detection on metallic surfaces. Comput Aided Civ Infrastruct Eng 32(4):271–287

    Article  Google Scholar 

  68. Mil S, Piantanakulchai M (2018) Modified Bayesian data fusion model for travel time estimation considering spurious data and traffic conditions. Appl Soft Comput 72:65–78

    Article  Google Scholar 

  69. Zhou T, Chen M, Yang C, Nie Z (2020) Data fusion using Bayesian theory and reinforcement learning method. Sci China Inf Sci 63:170209

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yongchuan Tang, Dongdong Wu & Zijing Liu

Authors
  1. Yongchuan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongdong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zijing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongchuan Tang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, Y., Wu, D. & Liu, Z. A new approach for generation of generalized basic probability assignment in the evidence theory. Pattern Anal Applic 24, 1007–1023 (2021). https://doi.org/10.1007/s10044-021-00966-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-021-00966-0

Keywords

Search

Navigation