Skip to main content
SpringerLink
Log in

Time series prediction based on high-order intuitionistic fuzzy cognitive maps with variational mode decomposition

  • Foundation, algebraic, and analytical methods in soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In reality, time series subject to the internal/external influence are usually characterized by nonlinearity, uncertainty, and incompleteness. Therefore, how to model the features of time series in nondeterministic environments is still an open problem. In this article, a novel high-order intuitionistic fuzzy cognitive map (HIFCM) is proposed, where intuitionistic fuzzy set (IFS) is introduced into fuzzy cognitive maps with temporal high-order structure. By means of IFS, the ability of model for the representation of uncertainty can be effectively improved. In order to capture the fluctuation features of series data, variational mode decomposition is utilized to decompose time series into sequences of various frequencies, based on which fine feature structures on different scales can be obtained. Each concept of HIFCM corresponds to one decomposed sequence such that casual reasoning can be achieved among the obtained features in various frequencies of time series. All parameters are learned by the particle swarm optimization algorithm. Finally, the performance of the method is verified on the public datasets, and experimental results show the feasibility and effectiveness 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

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Alci M, Asyali MH (2009) Nonlinear system identification via Laguerre network based fuzzy systems. Fuzzy Sets Syst 160(24):3518–3529

    Article  MathSciNet  Google Scholar 

  • Alghzawi AZ, Nápoles G, Sammour G et al (2017) Forecasting social security revenues in Jordan using fuzzy cognitive maps, pp 246–254

  • Atanassov KT (1999) Intuitionistic fuzzy sets. Physica-Verlag HD, Heidelberg

    Book  Google Scholar 

  • Bi X, Cao S, Zhang D (2019) A variety of engine faults detection based on optimized variational mode decomposition-robust independent component analysis and fuzzy C-mean clustering. IEEE Access 7:27756–27768

    Article  Google Scholar 

  • Deb C, Zhang F, Yang J et al (2017) A review on time series forecasting techniques for building energy consumption. Renew Sustain Energy Rev 74:902–924

    Article  Google Scholar 

  • Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3):531–544

    Article  MathSciNet  Google Scholar 

  • Foreman-Mackey D, Agol E, Ambikasaran S et al (2017) Fast and scalable Gaussian process modeling with applications to astronomical time series. Astron J 154(6):220

    Article  Google Scholar 

  • Froelich W, Pedrycz W (2017) Fuzzy cognitive maps in the modeling of granular time series. Knowl Based Syst 115:110–122

    Article  Google Scholar 

  • García S, Fernández A, Luengo L et al (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064

    Article  Google Scholar 

  • Geva AB (1998) ScaleNet-multiscale neural-network architecture for time series prediction. IEEE Trans Neural Netw 9(6):1471–1482

    Article  Google Scholar 

  • Hestenes MR (1969) Multiplier and gradient methods. J Optim Theor Appl 4(5):303–320

    Article  MathSciNet  Google Scholar 

  • Iakovidis DK, Papageorgiou E (2011) Intuitionistic fuzzy cognitive maps for medical decision making. IEEE Trans Inf Technol Biomed 15(1):100–107

    Article  Google Scholar 

  • Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans SMC 23(3):665–685

    Google Scholar 

  • Jaramillo J, Velasquez JD, Franco CJ et al (2017) Research in financial time series forecasting with SVM: contributions from literature. IEEE Latin Am Trans 15(1):145–153

    Article  Google Scholar 

  • Klepsch J, Klüppelberg C, Wei T (2016) Prediction of functional ARMA processes with an application to traffic data. Econom Stats 1:128–149

    MathSciNet  Google Scholar 

  • Kosko B (1986) Fuzzy cognitive maps. Int J Hum-Comput Stud Int J Man-Mach Stud 24(1):65–75

    Article  Google Scholar 

  • Kyriakarakos G, Dounis AI, Arvanitis KG et al (2017) Design of a fuzzy cognitive maps variable-load energy management system for autonomous PV-reverse osmosis desalination systems: a simulation survey. Appl Energy 187:575–584

    Article  Google Scholar 

  • Lee KC, Lee WJ et al (1998) Strategic planning simulation based on fuzzy cognitive map knowledge and differential game. SIMULATION 71(5):316–327

    Article  Google Scholar 

  • Li G, Ma X, Yang H (2018) A hybrid model for forecasting sunspots time series based on variational mode decomposition and backpropagation neural network improved by firefly algorithm. In: Computational intelligence and neuroscience

  • Liu Y, Yang C, Huang K et al (2020) Non-ferrous metals price forecasting based on variational mode decomposition and LSTM network, p 188

  • Liu Z, Liu J (2020) A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps. Knowl Based Syst 203:106105

    Article  Google Scholar 

  • Lu W, Yang J, Liu X et al (2014) The modelingand prediction of time series based on synergy of high-order fuzzy cognitive map and fuzzy c-means clustering. Knowl Based Syst 70:242–255

    Article  Google Scholar 

  • Luo C, Zhang N, Wang X (2020) Time series prediction based on intuitionistic fuzzy cognitive map. Soft Comput 24(9):6835–6850

    Article  Google Scholar 

  • Ma N, Yang BR, Qiu ZQ et al (2012) Progressive measure based fuzzy cognitive map and its application. Comput Eng Des 33(5):1958–1962

    Google Scholar 

  • Mackey M, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197(4300):287–289

    Article  Google Scholar 

  • Najafi A, Amirkhani A, Papageorgiou EI et al (2017) Medical decision making based on fuzzy cognitive map and a generalization linguistic weighted power mean for computing with words. In: IEEE international conference on fuzzy systems, pp 1–6

  • Olazabal M, Pascual U (2016) Use of fuzzy cognitive maps to study urban resilience and transformation. Environ Innov Soc Transit 18:18–40

    Article  Google Scholar 

  • Papageorgiou EI, Poczęta K, Laspidou C (2016) Hybrid model for water demand prediction based on fuzzy cognitive maps and artificial neural networks. In: IEEE international conference on fuzzy systems. IEEE, pp 1523–1530

  • Pedrycz W, Jastrzebska A, Homenda W (2016) Design of fuzzy cognitive maps for modeling time series. IEEE Trans Fuzzy Syst 24(1):120–130

    Article  Google Scholar 

  • Renaud O, Starck JL, Murtagh F (2005) Wavelet-based combined signal filtering and prediction. IEEE Trans Syst 35(6):1241–1251

    Google Scholar 

  • Salmeron JL, Rahimi SA, Navali AM et al (2017) Medical diagnosis of rheumatoid arthritis using data driven PSO-FCM with scarce datasets. Neurocomputing 232:104–112

    Article  Google Scholar 

  • Srivastava N, Hinton G, Krizhevsky A et al (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15(1):1929–1958

    MathSciNet  MATH  Google Scholar 

  • Vanhoenshoven F et al (2020) Pseudoinverse learning of fuzzy cognitive maps for multivariate time series forecasting. Appl Soft Comput 95:106461

    Article  Google Scholar 

  • Vilela LFS, Leme RC et al (2019) Forecasting financial series using clustering methods and support vector regression. Artif Intell Rev 52(2):743–773

    Article  Google Scholar 

  • Wang J, Peng Z, Wang X et al (2020) Deep fuzzy cognitive maps for interpretable multivariate time series prediction. In: IEEE transactions on fuzzy systems

  • Wu K, Liu J, Liu P et al (2019) Time series prediction using sparse autoencoder and high-order fuzzy cognitive maps. In: IEEE transactions on fuzzy systems

  • Yang S, Liu J (2018) Time series forecasting based on high-order fuzzy cognitive maps and wavelet transform. IEEE Trans Fuzzy Syst 26(6):1–1

    Article  Google Scholar 

  • Zadeh LA (1975) Fuzzy logic and approximate reasoning - in memory of Grigore Moisil. Synthese 30(3):407–428

    Article  Google Scholar 

  • Zadeh LA (2008) Is there a need for fuzzy logic? Inf Sci 178(13):2751–2779

    Article  MathSciNet  Google Scholar 

  • Zhang GF, He LH, Jiang YT et al (2013) Intuitionistic fuzzy cognitive map based on fuzzy measure and integral. In: International conference on machine learning and cybernetics, vol 1, pp 188–193

  • Zhang N, Luo C (2019) Adaptive online time series prediction based on a novel dynamic fuzzy cognitive map. J Intell Fuzzy Syst 36(1):1–13

    Article  Google Scholar 

  • Zheng G, Starck JL et al (1999) Multiscale transforms for filtering financial data streams. J Comput Intell Financ 7:18–35

    Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (62172264) and the Shandong Provincial Natural Science Foundation (ZR2019MF020).

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

    Yao Xixi, Ding Fengqian & Luo Chao

  2. Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan, 250014, China

    Luo Chao

Authors
  1. Yao Xixi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ding Fengqian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luo Chao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luo Chao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

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

Xixi, Y., Fengqian, D. & Chao, L. Time series prediction based on high-order intuitionistic fuzzy cognitive maps with variational mode decomposition. Soft Comput 26, 189–201 (2022). https://doi.org/10.1007/s00500-021-06455-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-06455-0

Keywords

Search

Navigation