Skip to main content
SpringerLink
Log in

Spatial–temporal fuzzy information granules for time series forecasting

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The prediction of time series in multi-steps is of significance in reality. However, considering the uncertainty and high noise existing in time series, the long-term forecasting is still an open problem. By means of granular computing, in this article, a novel spatial–temporal fuzzy information granule (STFIG) model is proposed to achieve the multi-step forecasting of time series. From the perspective of time dimension, by using unequal division method, time series is converted into generalized time-varying fuzzy information granules, where the trend information and dispersion degree of sequence data can be quantitatively described. Moreover, in terms of spatial dimension, the fluctuation information of time series is also calculated and involved into information granules, which can further enhance the semantic representation of sequential data. In order to improve the ability of dealing with uncertainties and fuzziness in time series, the interval type-2 fuzzy set is applied in the granules model. By using synthetic data and real-life time series, experiments are carried out to verify the effectiveness of the proposed scheme, where abundant semantic information and better long-term predictive performance can be obtained.

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Baklouti N, Abraham A, Alimi AM (2018) A Beta basis function Interval Type-2 Fuzzy Neural Network for time series applications. Eng Appl Artif Intell 71:259–274

    Article  Google Scholar 

  • Bromiley PA (2003) Products and convolutions of Gaussian distributions. Medical School, Univ. Manchester, Manchester, UK, Technical Report 2003, 3

  • Castillo O, Melin P, Tsvetkov R et al (2015) Short remark on fuzzy sets, interval type-2 fuzzy sets, general type-2 fuzzy sets and intuitionistic fuzzy sets. In: Intelligent systems’ 2014. Springer, Cham, pp 183–190

  • Chen SM, Hsu CC (2004) A new method to forecast enrollments using fuzzy time series. Int J Appl Sci Eng 2(3):234–244

    Google Scholar 

  • Chen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391:65–79

    Article  Google Scholar 

  • Colak I, Sagiroglu S, Yesilbudak M et al (2015) Multi-time series and-time scale modeling for wind speed and wind power forecasting part I: statistical methods, very short-term and short-term applications. In: 2015 international conference on renewable energy research and applications (ICRERA). IEEE, pp 209–214

  • Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292

    Article  Google Scholar 

  • Deng W, Liu H, Xu J, Zhao H, Song Y (2020a) An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2020.2983233

    Article  Google Scholar 

  • Deng W, Xu J, Song Y, Zhao H (2020b) An effective improved co-evolution ant colony optimization algorithm with multi-strategies and its application. Int J Bio-Inspired Comput 3(5):267–274

    Google Scholar 

  • Diamond P, Kloeden P (2000) Metric topology of fuzzy numbers and fuzzy analysis. Fundamentals of fuzzy sets. Springer, Boston, pp 583–641

    MATH  Google Scholar 

  • https://datamarket.com/data/set/22ox/monthly-milk-production-pounds-per-cow-jan-62-dec-75#!ds=22ox&display=line

  • https://datamarket.com/data/set/22ti/zuerich-monthly-sunspot-numbers-1749-1983#!ds=22ti&display=line

  • https://datamarket.com/data/set/2323/daily-maximum-temperatures-in-melbourne-australia-1981-1990#!ds=2323&display=line

  • Ji C, Zhao C, Liu S, Yang C, Pan L, Wu L, Meng X (2019a) A fast shapelet selection algorithm for time series classification. Comput Netw 148:231–240

    Article  Google Scholar 

  • Ji C, Zhao C, Pan L, Liu S, Yang C, Meng X (2019b) A just-in-time shapelet selection service for online time series classification. Comput Netw 157:89–98

    Article  Google Scholar 

  • Khanesar MA, Kayacan E, Teshnehlab M et al (2011) Extended Kalman filter based learning algorithm for type-2 fuzzy logic systems and its experimental evaluation. IEEE Trans Ind Electron 59(11):4443–4455

    Article  Google Scholar 

  • Lee LW, Wang LH, Chen SM et al (2006) Handling forecasting problems based on two-factors high-order fuzzy time series. IEEE Trans Fuzzy Syst 14(3):468–477

    Article  Google Scholar 

  • Li JQ, Song MX, Wang L, Duan PY, Han YY, Sang HY, Pan QK (2020) Hybrid artificial bee colony algorithm for parallel batching distributed flow-shop problem with deteriorating jobs. IEEE Trans Cybernet 50(6):2425–2439

    Article  Google Scholar 

  • Lin YY, Chang JY, Pal NR et al (2013) A mutually recurrent interval type-2 neural fuzzy system (MRIT2NFS) with self-evolving structure and parameters. IEEE Trans Fuzzy Syst 21(3):492–509

    Article  Google Scholar 

  • Lin L, Wang F, Xie X et al (2017) Random forests-based extreme learning machine ensemble for multi-regime time series prediction. Expert Syst Appl 83:164–176

    Article  Google Scholar 

  • Liu H, Xu B, Lu D, Zhang G (2018) A path planning approach for crowd evacuation in buildings based on improved artificial bee colony algorithm. Appl Soft Comput 68:360–376

    Article  Google Scholar 

  • Lu W, Chen X, Pedrycz W et al (2015) Using interval information granules to improve forecasting in fuzzy time series. Int J Approx Reason 57:1–18

    Article  Google Scholar 

  • Luo C, Tan C, Wang X, Zheng Y (2019a) An evolving recurrent interval type-2 intuitionistic fuzzy neural network for online learning and time series prediction. Appl Soft Comput 78:150–163

    Article  Google Scholar 

  • Luo C, Tan C, Zheng YJ (2019b) Long-term prediction of time series based on stepwise linear division algorithm and time-variant zonary fuzzy information granules. Int J Approx Reason 108:38–61

    Article  MathSciNet  Google Scholar 

  • Luo C, Song X, Zheng YJ (2020) A novel forecasting model for the long-term fluctuation of time series based on polar fuzzy information granules. Inf Sci 512:760–779

    Article  Google Scholar 

  • Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127

    Article  Google Scholar 

  • Pedrycz W, Vukovich G (2001) Abstraction and specialization of information granules. IEEE Trans Syst Man Cybernet Part B (Cybernet) 31(1):106–111

    Article  Google Scholar 

  • Shen Y, Pedrycz W et al (2018) Approximation of fuzzy sets by interval type-2 trapezoidal fuzzy sets. IEEE Trans Cybernet. https://doi.org/10.1109/TCYB.2018.2886725

    Article  Google Scholar 

  • Shuai Y, Song T, Wang J (2017) Integrated parallel forecasting model based on modified fuzzy time series and SVM. J Syst Eng Electron 28(4):766–775

    Article  Google Scholar 

  • Song Q, Chissom BS (1993) Fuzzy time series and its models. Fuzzy Sets Syst 54(3):269–277

    Article  MathSciNet  Google Scholar 

  • Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15:116–132

    Article  Google Scholar 

  • Wang L, Liu X, Pedrycz W (2013) Effective intervals determined by information granules to improve forecasting in fuzzy time series. Expert Syst Appl 40(14):5673–5679

    Article  Google Scholar 

  • Wang W, Pedrycz W, Liu X (2015) Time series long-term forecasting model based on information granules and fuzzy clustering. Eng Appl Artif Intell 41:17–24

    Article  Google Scholar 

  • Yang Q, Chen WN, Yu Z, Gu T, Li Y, Zhang H, Zhang J (2016) Adaptive multimodal continuous ant colony optimization. IEEE Trans Evol Comput 21(2):191–205

    Article  Google Scholar 

  • Yang X, Yu F, Pedrycz W (2017) Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system. Int J Approx Reason 81:1–27

    Article  MathSciNet  Google Scholar 

  • Yolcu U, Egrioglu E, Uslu VR et al (2009) A new approach for determining the length of intervals for fuzzy time series. Appl Soft Comput 9(2):647–651

    Article  Google Scholar 

  • Yu X, Chen WN, Gu TL et al (2018) Set-based discrete particle swarm optimization based on decomposition for permutation-based multiobjective combinatorial optimization problems. IEEE Trans Cybernet 48(7):2139–2153

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci 8(3):199–249

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1979) Fuzzy sets and information granularity. Adv Fuzzy Set Theory Appl 11:3–18

    MathSciNet  Google Scholar 

  • Zhang N, Luo C (2019) Adaptive online time series prediction based on a novel dynamic fuzzy cognitive map. J Intell Fuzzy Syst 36:5291–5303

    Article  Google Scholar 

  • Zhao H, Li D, Deng W, Yang X (2017) Research on vibration suppression method of alternating current motor based on fractional order control strategy. Proc Inst Mech Eng Part E J Process Mech Eng 231(4):786–799

    Article  Google Scholar 

  • Zheng X, Liu H (2010) A scalable co-evolutionary multi-objective particle swarm optimizer. Int J Comput Intell Syst 3(5):590–600

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (61402267); Shandong Provincial Natural Science Foundation (ZR2019MF020).

Author information

Authors and Affiliations

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

    Yuanyuan Zhao, Tingting Li & Chao Luo

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

    Chao Luo

Authors
  1. Yuanyuan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tingting Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chao Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao Luo.

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

Communicated by V. Loia.

Publisher's Note

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

Appendix A: The last 30 STFIGs in the Experiment 5 (2)

Appendix A: The last 30 STFIGs in the Experiment 5 (2)

information granule

Real parameters

 

Forecast parameters

a

b

c

σ

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{c} \)

\( \bar{c} \)

,

a

b

c

σ

\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{c} \)

\( \bar{c} \)

A 953

− 0.0182

− 0.1643

3106.81

0.92

3105.73

3107.84

,

− 0.0070

− 0.3334

3093.38

0.74

3092.53

3094.33

A 954

0.0169

− 0.2038

3099.72

1.06

3097.77

3100.85

,

− 0.0096

0.6675

3110.71

0.92

3109.83

3111.92

A 955

− 0.1113

0.9354

3094.60

0.92

3093.82

3095.58

,

− 0.0366

− 0.1954

3112.58

0.70

3111.75

3113.4

A 956

− 0.1835

2.5130

3090.40

0.63

3089.86

3090.96

,

− 0.0375

− 0.0538

3101.59

0.67

3100.76

3102.41

A 957

− 0.0009

− 0.176

3098.66

0.96

3096.83

3100.42

,

− 0.017

0.2050

3111.33

0.82

3110.43

3112.45

A 958

− 0.0936

1.2301

3092.17

0.30

3091.86

3092.32

,

− 0.0159

0.4038

3087.13

0.72

3086.47

3088.07

A 959

− 0.012

− 0.2393

3096.02

0.94

3095.07

3097.18

,

− 0.0577

0.1283

3101.68

1.04

3100.03

3103.33

A 960

0.0142

0.1113

3089.31

0.97

3087.9

3090.26

,

0.0278

0.0221

3079.63

1.21

3078.54

3081.30

A 961

0.0072

− 0.2038

3097.04

0.64

3096.33

3097.68

,

− 0.3571

0.8065

3091.61

0.81

3090.54

3092.65

A 962

0.0112

0.8654

3093.90

1.02

3092.76

3095.26

,

0.0206

0.0630

3081.6

1.09

3080.39

3083.17

A 963

0.0036

− 0.3666

3110.29

0.60

3109.45

3111.33

,

− 0.0353

− 0.4136

3085.73

1.42

3084.16

3087.52

A 964

0.0371

0.0611

3103.53

0.73

3103.06

3104.21

,

− 0.0005

0.6275

3109.75

1.16

3108.25

3111.77

A 965

0.0032

− 0.2542

3104.73

0.85

3103.04

3106.46

,

− 0.0256

− 0.1619

3094.53

0.6

3093.79

3095.21

A 966

0.0320

− 0.2008

3099.79

0.84

3098.59

3100.52

,

− 0.1025

1.5387

3097.45

0.72

3096.74

3098.24

A 967

− 0.0921

− 0.0661

3104.34

0.41

3103.94

3104.60

,

− 0.1804

0.8675

3103.76

0.55

3103.13

3104.24

A 968

− 0.0398

0.8028

3101.00

0.61

3100.52

3101.65

,

− 0.0317

0.3632

3100.61

0.66

3099.85

3101.46

A 969

− 0.0002

− 0.3027

3103.53

1.23

3100.99

3105.17

,

− 0.0307

− 0.1239

3112.45

0.73

3111.63

3113.26

A 970

0.0136

0.2685

3095.30

2.19

3093.08

3098.55

,

0.0269

0.0104

3084.27

1.05

3083.11

3085.69

A 971

0.0020

− 0.3023

3107.33

0.78

3106.09

3108.40

,

− 0.0650

0.0265

3070.65

0.99

3069.17

3072.09

A 972

0.0020

0.3488

3097.72

0.65

3096.88

3098.26

,

0.0101

0.3257

3092.74

1.19

3091.08

3094.61

A 973

− 0.0218

0.2248

3100.62

0.63

3100.09

3101.47

,

− 0.1117

− 0.0202

3108.07

0.60

3107.37

3108.72

A 974

− 0.0673

0.9637

3097.49

0.29

3097.15

3097.67

,

− 0.0105

0.3779

3110.45

0.38

3110.01

3110.84

A 975

− 0.0318

0.3180

3099.14

0.78

3098.33

3100.01

,

− 0.0616

0.0197

3114.82

0.61

3114.03

3115.53

A 976

− 0.0035

0.2488

3095.09

0.62

3094.40

3096.06

,

− 0.0034

0.3014

3106.25

0.70

3105.44

3107.07

A 977

− 0.0234

0.2282

3098.95

0.54

3098.45

3099.43

,

0.0144

− 0.5952

3114.56

1.06

3113.27

3115.92

A 978

− 0.0505

0.9694

3098.36

0.53

3097.82

3098.82

,

− 0.0233

0.2133

3106.51

0.58

3105.88

3107.26

A 979

− 0.0925

0.3175

3102.05

0.26

3101.87

3102.24

,

− 0.0323

0.3069

3099.60

0.78

3098.76

3100.46

A 980

0.0107

− 0.0296

3102.67

0.43

3102.12

3103.10

,

− 0.0025

0.2352

3097.05

0.65

3096.32

3098.03

A 981

− 0.0005

− 0.3472

3106.52

1.27

3104.01

3109.17

,

0.0142

− 0.4325

3118.56

0.74

3117.64

3119.39

A 982

0.0133

0.1401

3093.92

1.32

3092.46

3095.89

,

− 0.0013

0.0994

3106.42

0.79

3105.48

3107.44

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Y., Li, T. & Luo, C. Spatial–temporal fuzzy information granules for time series forecasting. Soft Comput 25, 1963–1981 (2021). https://doi.org/10.1007/s00500-020-05268-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05268-x

Keywords

Search

Navigation