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Combining time-series evidence: A complex network model based on a visibility graph and belief entropy

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Abstract

Combining basic probability assignments (BPAs) with time series is common in real-life cases. Therefore, a new evidence fusion approach based on belief entropy and a visibility graph (BE-VG) is proposed. The approach converts a time-series BPA into a weighted visibility graph (WVG). In addition, some numerical examples are illustrated to illustrate the efficiency and applicability of the proposed method. Finally, to demonstrate the effect of the BE-VG method, the proposed method is applied to electroencephalogram (EEG) dynamic fusion. Experimentally, the results indicate that the BE-VG method is effective and accurate in conducting EEG signal fusion.

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Notes

  1. For two matrices A and B of the same dimension m × n, the Hadamard product A ∘ B is a matrix of the same dimension as the operands, with elements given by (A ∘ B)ij = (A)ij(B)ij.

References

  1. Cao Z, Ding W, Wang YK, Hussain F, Al-Jumaily A, Lin CT (2020) Effects of repetitive SSVEPs on EEG complexity using multiscale inherent fuzzy entropy. Neurocomputing 389:198–206

    Article  Google Scholar 

  2. Cao Z, Lin C, Lai K, Ko L, King J, Liao K, Fuh J, Wang S (2020) Extraction of SSVEPs-based inherent fuzzy entropy using a wearable headband EEG in migraine patients. IEEE Trans Fuzzy Syst 28(1):14–27

    Article  Google Scholar 

  3. Chang L, Zhang L, Fu C, Chen YW (2021) Transparent digital twin for output control using belief rule base. IEEE Transactions on Cybernetics https://doi.org/10.1109/TCYB.2021.3063285

  4. Chen D, Xie H (2021) Fire safety evaluation for scenic spots: An evidential best-worst method. Journal of Mathematics 2021, https://doi.org/10.1155/2021/5592,150

  5. Chen L, Deng Y, Cheong KH (2021) Probability transformation of mass function: a weighted network method based on the ordered visibility graph. Eng Appl Artif Intell 105(104):438

    Google Scholar 

  6. Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 325–339

  7. Deng J, Deng Y, Cheong KH (2021) Combining conflicting evidence based on pearson correlation coefficient and weighted graph. International Journal of Intelligent Systems https://doi.org/10.1002/int.22593

  8. Deng X, Jiang W (2019) On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation. Inf Sci 516:346–352

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng Y (2020) Information volume of mass function. Int J Comput Commun Control 15(6):3983

    Article  Google Scholar 

  10. Ding R, Palomares I, Wang X, Yang G, Liu B, Dong Y, Herrera-Viedma E, Herrera F (2020) Large-scale decision-making: characterization, taxonomy, challenges and future directions from an artificial intelligence and applications perspective. Inform Fusion 59:84–102

    Article  Google Scholar 

  11. Fei L, Lu J, Feng Y (2020) An extended best-worst multi-criteria decision-making method by belief functions and its applications in hospital service evaluation. Comput Indust Eng 142(106):355

    Google Scholar 

  12. Feng F, Cho J, Pedrycz W, Fujita H, Herawan T (2016) Soft set based association rule mining. Knowl-Based Syst 111:268– 282

    Article  Google Scholar 

  13. Fu C, Xue M, Xu D, Yang S (2019) Selecting strategic partner for tax information systems based on weight learning with belief structures. Int J Approx Reason 105:66–84

    Article  MathSciNet  MATH  Google Scholar 

  14. Fujita H, Cimr D (2019) Decision support system for arrhythmia prediction using convolutional neural network structure without preprocessing. Appl Intell 49:3383–3391

    Article  Google Scholar 

  15. Fujita H, Gaeta A, Loia V, Orciuoli F (2019) Improving awareness in early stages of security analysis: A zone partition method based on GrC. Appl Intell 49:1063–1077

    Article  Google Scholar 

  16. Fujita H, Gaeta A, Loia V, Orciuoli F (2020) Hypotheses analysis and assessment in counterterrorism activities: a method based on OWA and fuzzy probabilistic rough sets. IEEE Trans Fuzzy Syst 28 (5):831–845

    Article  Google Scholar 

  17. Fujita H, Ko YC (2020) A heuristic representation learning based on evidential memberships: Case study of UCI-SPECTF. Int J Approx Reason 120:125–137

    Article  MathSciNet  MATH  Google Scholar 

  18. Gao X, Su X, Qian H, Pan X (2021) Dependence assessment in Human Reliability Analysis under uncertain and dynamic situations. Nuclear Engineering and Technology

  19. Garg H, Chen S (2020) Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets. Inf Sci 517:427–447

    Article  MathSciNet  MATH  Google Scholar 

  20. Greff K, Srivastava RK, Koutnik J, Steunebrink BR, Schmidhuber J (2017) LSTM: A search space odyssey. IEEE Trans Neural Netw Learn Syst 28(10):2222–2232

    Article  MathSciNet  Google Scholar 

  21. Jiang W, Cao Y, Deng X (2020) A novel Z-network model based on Bayesian network and Z-number. IEEE Trans Fuzzy Syst 28(8):1585–1599

    Article  Google Scholar 

  22. Kang B, Zhang P, Gao Z, Chhipi-Shrestha G, Hewage K, Sadiq R (2019) Environmental assessment under uncertainty using Dempster-Shafer theory and Z-numbers. J Ambient Intell Humanized Comput 11:2041–2060

    Article  Google Scholar 

  23. Lacasa L, Just W (2018) Visibility graphs and symbolic dynamics. Physica D: Nonlinear Phenomena 35–44

  24. Lacasa L, Luque B, Ballesteros F, Luque J, Nuno JC (2008) From time series to complex networks: The visibility graph. Proc Natl Acad Sci USA 105(13):4972

    Article  MathSciNet  MATH  Google Scholar 

  25. Lai JW, Chang J, Ang L, Cheong KH (2020) Multi-level information fusion to alleviate network congestion. Inform Fusion 63:248–255

    Article  Google Scholar 

  26. Liao H, Ren Z, Fang R (2020) A Deng-entropy-based evidential reasoning approach for multi-expert multi-criterion decision-making with uncertainty. Int J Comput Intell Syst 13(1):1281–1294

    Article  Google Scholar 

  27. Liu F, Wang Z, Deng Y (2020) GMM: A generalized mechanics model for identifying the importance of nodes in complex networks. Knowl-Based Syst 193(105):464

    Google Scholar 

  28. Liu G, Xiao F (2019) A data-driven dynamic data fusion method based on visibility graph and evidence theory. IEEE Access 7:104,443–104,452

    Article  Google Scholar 

  29. Liu P, Zhang X, Pedrycz W (2020) A consensus model for hesitant fuzzy linguistic group decision-making in the framework of Dempster–Shafer evidence theory. Knowl-Based Syst 212(106):559

    Google Scholar 

  30. Liu Q, Tian Y, Kang B (2019) Derive knowledge of Z-number from the perspective of Dempster-Shafer evidence theory. Eng Appl Artif Intell 85:754–764

    Article  Google Scholar 

  31. Liu Z, Li G, Mercier G, He Y, Pan Q (2017) Change detection in heterogenous remote sensing images via homogeneous pixel transformation. IEEE Trans Image Process 27(4):1822– 1834

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu Z, Pan Q, Dezert J, Han JW, He Y (2018) Classifier fusion with contextual reliability evaluation. IEEE Trans Cybern 48(5):1605–1618

    Article  Google Scholar 

  33. Long H, Peng Z, Deng Y (2021) A new structure of the focal element in object recognition. International Journal of Intelligent Systems https://doi.org/10.1002/int.2267

  34. Meng D, Xie T, Wu P, He C, Hu Z, Lv Z (2021) An uncertainty-based design optimization strategy with random and interval variables for multidisciplinary engineering systems. In: Structures, vol 32. Elsevier, pp 997–1004

  35. Meng D, Xie T, Wu P, Zhu SP, Hu Z, Li Y (2020) Uncertainty-based design and optimization using first order saddle point approximation method for multidisciplinary engineering systems. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part A: Civil Engineering 6(3):04020,028

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  37. Shang QY, Deng Y, Cheong KH (2021) Identifying influential nodes in complex networks: Effective distance gravity model. Inf Sci 577:162–179

    Article  MathSciNet  Google Scholar 

  38. Smets P (2007) Analyzing the combination of conflicting belief functions. Inform Fusion 8 (4):387–412

    Article  Google Scholar 

  39. Song Y, Deng Y (2021) Entropic explanation of power set. Int J Comput Commun Control 16(4):4413. https://doi.org/10.15837/ijccc.2021.4.4413

    Article  Google Scholar 

  40. Song Y, Fu Q, Wang Y, Wang X (2019) Divergence-based cross entropy and uncertainty measures of Atanassov’s intuitionistic fuzzy sets with their application in decision making. Appl Soft Comput 84 (105):703

    Google Scholar 

  41. Tang M, Liao H, Herrera-Viedma E, Chen CP, Pedrycz W (2020) A dynamic adaptive subgroup-to-subgroup compatibility-based conflict detection and resolution model for multicriteria large-scale group decision making. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2020.2974924

  42. Verano DA, Husnawati H, Ermatita E (2020) Implementation of autoregressive integrated moving average model to forecast raw material stock in the digital printing industry. J Inform Technol Comput Sci 5 (1):13

    Google Scholar 

  43. Wang C, Koh JM, Cheong KH, Xie NG (2019) Progressive information polarization in a complex-network entropic social dynamics model. IEEE Access 7:35,394–35,404

    Article  Google Scholar 

  44. Wen T, Pelusi D, Deng Y (2020) Vital spreaders identification in complex networks with multi-local dimension. Knowl-Based Syst 195(105):717

    Google Scholar 

  45. Xiao B, Xu W, Guo J, Lam HK, Ren H (2020) Depth estimation of hard inclusions in soft tissue by autonomous robotic palpation using deep recurrent neural network. IEEE Trans Autom Sci Eng PP (99):1–9

    Google Scholar 

  46. Xiao F (2020) CEQD: A complex mass function to predict interference effects. IEEE Transactions on Cybernetics https://doi.org/10.1109/TCYB.2020.3040770

  47. Xiao F (2020) Evidence combination based on prospect theory for multi-sensor data fusion. ISA Trans 106:253–261

    Article  Google Scholar 

  48. Xiao F (2021) On the maximum entropy negation of a complex-valued distribution. IEEE Transactions on Fuzzy Systems 29(11):3259–3269

    Article  Google Scholar 

  49. Xiao F (2021) CaFtR: A fuzzy complex event processing method. International Journal of Fuzzy Systems DOI10.1007/s40,815–021–01,118–6

  50. Xiao F (2021) CED: A distance for complex mass functions. IEEE Trans Neural Netw Learn Syst 32(4):1525–1535

    Article  MathSciNet  Google Scholar 

  51. Xiao F (2021) GIQ: A generalized intelligent quality-based approach for fusing multi-source information. IEEE Trans Fuzzy Syst 29(7):2018–2031

    Article  Google Scholar 

  52. Xiong L, Su X, Qian H (2021) Conflicting evidence combination from the perspective of networks. Inf Sci 580:408–418

    Article  MathSciNet  Google Scholar 

  53. Xu X, Xu H, Wen C, Li J, Hou P, Zhang J (2018) A belief rule-based evidence updating method for industrial alarm system design. Control Eng Pract 81:73–84

    Article  Google Scholar 

  54. Xu X, Zheng J, Yang J, Xu D, Chen Y (2017) Data classification using evidence reasoning rule. Knowl-Based Syst 116:144– 151

    Article  Google Scholar 

  55. Xue Y, Deng Y (2021) Interval-valued belief entropies for Dempster Shafer structures. Soft Comput 25:8063–8071

    Article  Google Scholar 

  56. Ye Y, Hang XR, Koh JM, Miszczak JA, Cheong KH (2020) Xie, N.g.: Passive network evolution promotes group welfare in complex networks. Chaos, Solitons & Fractals 130(109):464

    MATH  Google Scholar 

  57. Zhao J, Deng Y (2020) Complex network modeling of evidence theory. IEEE Transactions on Fuzzy Systems https://doi.org/10.1109/TFUZZ.2020.3023760

  58. Zhou M, Liu X, Chen Y, Yang J (2018) Evidential reasoning rule for MADM with both weights and reliabilities in group decision making. Knowl-Based Syst 143:142–161

    Article  Google Scholar 

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Acknowledgements

The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. This research is supported by the National Natural Science Foundation of China (No. 62003280).

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

    Xingjian Song & Fuyuan Xiao

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  1. Xingjian Song
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Song, X., Xiao, F. Combining time-series evidence: A complex network model based on a visibility graph and belief entropy. Appl Intell 52, 10706–10715 (2022). https://doi.org/10.1007/s10489-021-02956-5

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