Skip to main content
SpringerLink
Log in

Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

Intuitionistic fuzzy sets are extended form of type 1 fuzzy sets. The modeling methods use intuitionistic fuzzy sets have second-order uncertainty approximation so these methods may have better results than methods based on type-1 fuzzy sets. Intuitionistic fuzzy sets have been used in forecasting methods and these methods are called intuitionistic fuzzy time series forecasting methods. In this study, new intuitionistic fuzzy time series definitions are made and a new forecasting method is proposed based on intuitionistic fuzzy sets. The first contribution of the paper is to make new fuzzy and intuitionistic fuzzy time series definitions. The second contribution is to make new forecasting model definitions for fuzzy and intuitionistic fuzzy time series. The last contribution is to propose a forecasting method for single-variable high-order intuitionistic fuzzy time series forecasting model. In the proposed method, fuzzification of observations is done by using intuitionistic fuzzy c-means algorithm and fuzzy relations are defined by pi-sigma artificial neural networks. Artificial bee colony algorithm is used to train Pi-Sigma artificial neural network in the proposed method. Real-world time series applications have been made for exploring performance 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
Fig. 9

Similar content being viewed by others

References

  • Abhishekh S, Gautam SS, Singh SR (2018a) A score function-based method of forecasting using intuitionistic fuzzy time series. N Math Nat Comput 14(1):91–111

    Article  MathSciNet  Google Scholar 

  • Abhishekh S, Gautam SS, Singh SR (2018b) A refined weighted method for forecasting based on type 2 fuzzy time series. Int J Model Simul 38(3):180–188

    Article  Google Scholar 

  • Aladag CH (2013) Using multiplicative neuron model to establish fuzzy logic relationships. Expert Syst. Appl. 40:850–853

    Article  Google Scholar 

  • Aladag CH, Basaran MA, Egrioglu E, Yolcu U, Uslu VR (2009) Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Syst Appl 36(3 part 1):4228–4231

    Article  Google Scholar 

  • Askari S, Montazerin N (2015) A high-order multi-variable fuzzy time series forecasting algorithm based on fuzzy clustering. Expert Syst Appl 42(4):2121–2135

    Article  Google Scholar 

  • Atanassov K (1983) Intuitionistic fuzzy sets. In: Proc. VII ITKR’s Session, Sofia, June 1684–1697

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Atanassov K (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  • Bai E, Wong WK, Chu WC, Xia M, Pan F (2011) A heuristic time-invariant model for fuzzy time series forecasting. Expert Syst Appl 38(3):2701–2707

    Article  Google Scholar 

  • Bajestani NS, Zare A (2011) Forecasting TAIEX using improved type 2 fuzzy time series. Expert Syst Appl 38(5):5816–5821

    Article  Google Scholar 

  • Bas E, Egrioglu E, Aladag CH, Yolcu U (2015) Fuzzy-time-series network used to forecast linear and nonlinear time series. Appl Intell 43:343–355

    Article  Google Scholar 

  • Bas E, Grosan C, Egrioglu E, Yolcu U (2018) High order fuzzy time series method based on Pi-Sigma neural network. Eng Appl Artif Intell 72:350–356

    Article  Google Scholar 

  • Bisht K, Kumar S (2016) Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Syst Appl 64:557–568

    Article  Google Scholar 

  • Bisht K, Joshi DK, Kumar S (2018) Dual hesitant fuzzy set-based intuitionistic fuzzy time series forecasting. Adv Intell Syst Comput 696:317–329

    Google Scholar 

  • Bulut E (2014) Modeling seasonality using the fuzzy integrated logical forecasting (FILF) approach. Expert Syst Appl 41:1806–1812

    Article  Google Scholar 

  • Cagcag Yolcu O, Alpaslan F (2018) Prediction of TAIEX based on hybrid fuzzy time series model with single optimization process. Appl Soft Comput J 66:18–33

    Article  Google Scholar 

  • Chaira T (2011) A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Appl Soft Comput 11(2):1711–1717

    Article  Google Scholar 

  • Chen SM (1996) Forecasting enrollments based on fuzzy time-series. Fuzzy Sets Syst 81:311–319

    Article  Google Scholar 

  • Chen SM, Chang YC (2011) Weighted fuzzy rule interpolation based on GA-based weight-learning techniques. IEEE Trans Fuzzy Syst 19(4):729–744

    Article  MathSciNet  Google Scholar 

  • Chen S-M, Chen C-D (2011) Handling forecasting problems based on high-order fuzzy logical relationships. Expert Syst Appl 38(4):3857–3864

    Article  Google Scholar 

  • Chen S-M, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216

    Article  Google Scholar 

  • Chen SM, Tanuwijaya K (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437

    Article  Google Scholar 

  • Chen SM, Lee SH, Lee CH (2001) A new method for generating fuzzy rules from numerical data for handling classification problems. Appl Artif Intell 15(7):645–664

    Article  Google Scholar 

  • Chen S-M, Wang N-Y, Pan J-S (2009) Forecasting enrollments using automatic clustering techniques and fuzzy logical relationships. Expert Syst Appl 36(8):11070–11076

    Article  Google Scholar 

  • Chen SM, Munif A, Chen GS, Liu HC, Kuo (2012) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst Appl 39(7):6320–6334

    Article  Google Scholar 

  • Cheng C-H, Chen C-H (2018) Fuzzy time series model based on weighted association rule for financial market forecasting. Expert Syst. https://doi.org/10.1111/exsy.12271 (article in press)

    Article  Google Scholar 

  • Cheng C-H, Yang J-H (2018) Fuzzy time-series model based on rough set rule induction for forecasting stock price. Neurocomputing 302:33–45

    Article  Google Scholar 

  • Cheng C-H, Chen Y-S, Wu Y-L (2009) Forecasting innovation diffusion of products using trend-weighted fuzzy time-series model. Expert Syst Appl 36(2 part 1):1826–1832

    Article  Google Scholar 

  • Domańska D, Wojtylak M (2012) Application of fuzzy time series models for forecasting pollution concentrations. Expert Syst Appl 39(9):7673–7679

    Article  Google Scholar 

  • Duru O (2010) A fuzzy integrated logical forecasting model for dry bulk shipping index forecasting: An improved fuzzy time series approach. Expert Syst Appl 37(7):5372–5380

    Article  Google Scholar 

  • Duru O (2012) A multivariate model of fuzzy integrated logical forecasting method (M-FILF) and multiplicative time series clustering: a model of time-varying volatility for dry cargo freight market. Expert Syst Appl 39(4):4135–4142

    Article  Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Basaran MA (2009a) A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst Appl 36(7):10589–10594

    Article  Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U, Basaran MA, Uslu VR (2009b) A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model. Expert Syst Appl 36(4):7424–7434

    Article  Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Basaran MA (2010) Finding an optimal interval length in high order fuzzy time series. Expert Syst Appl 37(7):5052–5055

    Article  Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Erilli NA (2011) Fuzzy time series forecasting method based on Gustafson–Kessel fuzzy clustering. Expert Syst Appl 38(8):10355–10357

    Article  Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U (2013) Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks. Expert Syst Appl 40(3):854–857

    Article  Google Scholar 

  • Fan X-S, Lei Y-J, Lu Y-L, Wang Y-N (2016a) Long-term intuitionistic fuzzy time series forecasting model based on DTW. Tongxin Xuebao/J Commun 37(8):95–104

    Google Scholar 

  • Fan X, Lei Y, Wang Y, Lu Y (2016b) Long-term intuitionistic fuzzy time series forecasting model based on vector quantisation and curve similarity measure. IET Signal Proc 10(7):805–814

    Article  Google Scholar 

  • Fan X, Lei Y, Wang Y (2017) Adaptive partition intuitionistic fuzzy time series forecasting model. J Syst Eng Electron 28(3):585–596

    Google Scholar 

  • Gangwar SS, Kumar S (2012) Partitions based computational method for high-order fuzzy time series forecasting. Expert Syst Appl 39(15):12158–12164

    Article  Google Scholar 

  • Guler Dincer N, Akkus O (2018) A new fuzzy time series model based on robust clustering for forecasting of air pollution. Ecol Inform 43:157–164

    Article  Google Scholar 

  • Guo H, Pedrycz W, Liu X (2018) Fuzzy time series forecasting based on axiomatic fuzzy set theory. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3325-9 (article in press)

    Article  Google Scholar 

  • Gupta KK, Kumar S (2018) Hesitant probabilistic fuzzy set based time series forecasting method. Granul Comput. https://doi.org/10.1007/s41066-018-0126-1

    Article  Google Scholar 

  • Hsu L-Y, Horng S-J, Kao T-W, Chen Y-H, Run R-S, Chen R-J, Lai J-L, Kuo I-H (2010) Temperature prediction and TAIFEX forecasting based on fuzzy relationships and MTPSO techniques. Expert Syst Appl 37(4):756–2770

    Google Scholar 

  • Hu D, Zan L, Chen X, Jie W (2017) Prediction of satellite clock errors based on deterministic intuitionistic fuzzy time series. In: International conference on signal processing proceedings ICSP, 1006–1009

  • Joshi BP, Pandey M, Kumar S (2016) Use of intuitionistic fuzzy time series in forecasting enrollments to an academic institution. Adv Intell Syst Comput 436:843–852

    Google Scholar 

  • Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. TR-06, Erciyes University, Engineering Faculty, Computer Engineering Department

  • Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214:108–132

    MathSciNet  MATH  Google Scholar 

  • Kocak C (2017) ARMA (p,q) type high order fuzzy time series forecast method based on fuzzy logic relations. Appl Soft Comput 58:92–103

    Article  Google Scholar 

  • Kumar S, Gangwar SS (2016) Intuitionistic fuzzy time series: an approach for handling nondeterminism in time series forecasting. IEEE Trans Fuzzy Syst 24(6):1270–1281

    Article  Google Scholar 

  • Kuo I-H, Horng S-J, Kao T-W, Lin T-L, Lee C-L, Pan Y (2009) An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization. Expert Syst Appl 36(3 part 2):6108–6117

    Article  Google Scholar 

  • Kuo I-H, Horng S-J, Chen Y-H, Run R-S, Kao T-W, Chen R-J, Lai J-L, Lin T-L (2010) Forecasting TAIFEX based on fuzzy time series and particle swarm optimization. Expert Syst Appl 37(2):1494–1502

    Article  Google Scholar 

  • Leu Y, Lee C-P, Jou Y-Z (2009) A distance-based fuzzy time series model for exchange rates forecasting. Expert Syst Appl 36(4):8107–8114

    Article  Google Scholar 

  • Liu H-T, Wei M-L (2010) An improved fuzzy forecasting method for seasonal time series. Expert Syst Appl 37(9):6310–6318

    Article  Google Scholar 

  • Maciel L, Ballini R, Gomide F (2016) Evolving granular analytics for interval time series forecasting. Granul Comput 1(4):213–224

    Article  Google Scholar 

  • Qiu W. Liu X, Li HA (2011) Generalized method for forecasting based on fuzzy time series. Expert Syst Appl 38(8):10446–10453

    Article  Google Scholar 

  • Qiu W, Liu X, Wang L (2012) Forecasting shanghai composite index based on fuzzy time series and improved C-fuzzy decision trees. Expert Syst Appl 39(9):7680–7689

    Article  Google Scholar 

  • Rubio A, Bermúdez JD, Vercher E (2017) Improving stock index forecasts by using a new weighted fuzzy-trend time series method. Expert Syst Appl 76:12–20

    Article  Google Scholar 

  • Shin Y, Gosh J (1991) The Pi-sigma network: an efficient higher-order neural network for pattern classification and function approximation. In: Proceedings of the international joint conference on neural networks

  • 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

    Google Scholar 

  • Singh P (2018) Rainfall and financial forecasting using fuzzy time series and neural networks based model. Int J Mach Learn Cybern 9(3):491–506

    Article  Google Scholar 

  • Singh P, Dhiman G (2018) A hybrid fuzzy time series forecasting model based on granular computing and bio-inspired optimization approaches. J Comput Sci. https://doi.org/10.1016/j.jocs.2018.05.008 (article in press)

    Article  Google Scholar 

  • Song Q, Chissom BS (1993) Forecasting enrollments with fuzzy time series—part I. Fuzzy Sets Syst 54:1–10

    Article  Google Scholar 

  • Teoh HJ, Chen T-L, Cheng C-H, Chu H-H (2009) A hybrid multi-order fuzzy time series for forecasting stock markets. Expert Syst Appl 36(4):7888–7897

    Article  Google Scholar 

  • Tsaur R-C, Kuo T-C (2011) The adaptive fuzzy time series model with an application to Taiwan’s tourism demand. Expert Syst Appl 38(8):9164–9171

    Article  Google Scholar 

  • Wang HY, Chen SM (2008) Evaluating students’ answer scripts using fuzzy numbers associated with degrees of confidence. IEEE Trans Fuzzy Syst 16(2):403–415

    Article  Google Scholar 

  • Wang N-Y, Chen S-M (2009) Temperature prediction and TAIFEX forecasting based on automatic clustering techniques and two-factors high-order fuzzy time series. Expert Syst Appl 36(2 part 1):2143–2154

    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 L, Liu X, Pedrycz W, Shao Y (2014) Determination of temporal information granules to improve forecasting in fuzzy time series. Expert Syst Appl 41(6):3134–3142

    Article  Google Scholar 

  • Wang Y, Lei Y, Fan X, Wang Y (2016a) Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Math Probl Eng 2016:5035160. https://doi.org/10.1155/2016/5035160

    MathSciNet  MATH  Google Scholar 

  • Wang Y-N, Lei Y-J, Lei Y, Fan X-S (2016b) High order intuitionistic fuzzy time series forecasting model. Tongxin Xuebao/J Commun 37(5):115–124

    MATH  Google Scholar 

  • Wang Y, Lei Y, Lei Y, Fan X (2016c) High-order multi-variable intuitionistic fuzzy time series forecasting model. Dongnan Daxue Xuebao (Ziran Kexue Ban)/J Southeast Univ (Natural Science Edition) 46(3):505–512

    MathSciNet  MATH  Google Scholar 

  • Wang Y, Lei Y, Wang Y, Zheng K (2016d) A heuristic adaptive-order intuitionistic fuzzy time series forecasting model. Dianzi Yu Xinxi Xuebao/J Electron Inf Technol 38(11):2795–2802

    Google Scholar 

  • Wang Y, Lei Y, Lei Y, Fan X (2016e) Multi-factor high-order intuitionistic fuzzy time series forecasting model. J Syst Eng Electron 27(5):1054–1062

    Article  MATH  Google Scholar 

  • Wong H-L, Tu Y-H, Wang C-C (2010) Application of fuzzy time series models for forecasting the amount of Taiwan export. Expert Syst Appl 37(2):1465–1470

    Article  Google Scholar 

  • Xian S, Zhang J, Xiao Y, Pang J (2018) A novel fuzzy time series forecasting method based on the improved artificial fish swarm optimization algorithm. Soft Comput 22(12):3907–3917

    Article  Google Scholar 

  • Xu Z, Chen J, Wu J (2008) Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 178:(19)775–3790

    MathSciNet  MATH  Google Scholar 

  • Yolcu U, Cagcag Yolcu O, Aladag CH, Egrioglu E (2014) An enhanced fuzzy time series forecasting method based on artificial bee colony. J Intell Fuzzy Syst 26(6):2627–2637

    MathSciNet  Google Scholar 

  • Yu TH-K, Huarng K-H (2010) A neural network-based fuzzy time series model to improve forecasting. Expert Syst Appl 37(4):3366–3372

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zhang HM, Xu ZS, Chen Q (2007) On clustering approach to intuitionistic fuzzy sets. Control Decis 22(8):882–888

    MathSciNet  MATH  Google Scholar 

  • Zheng K-Q, Lei Y-J, Wang R, Wang Y (2013a) Prediction of IFTS based on deterministic transition.Yingyong Kexue. Xuebao/J Appl Sci 31(2):204–211

    Google Scholar 

  • Zheng K-Q, Lei Y-J, Wang R, Wang Y-F (2013b) Modeling and application of IFTS. Kongzhi yu Juece/Control Decis 28(10):1525–1530

    MATH  Google Scholar 

  • Zheng K-Q, Lei Y-J, Wang R, Xing Y-Q (2014a) Method of long-term IFTS forecasting based on parameter adaptation. Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Syst Eng Electron 36(1):99–104

    MATH  Google Scholar 

  • Zheng K-Q, Lei Y-J, Wang R, Yu X-D (2014b) Long-term intuitionistic fuzzy time series forecasting based on vector quantization. Jilin Daxue Xuebao (Gongxueban)/J Jilin Univ (Engineering and Technology Edition) 44 (3):795–800

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Forecast Research Laboratory, Department of Statistics, Faculty of Arts and Science, Giresun University, 28200, Giresun, Turkey

    Erol Egrioglu & Eren Bas

  2. Forecast Research Laboratory, Department of Econometrics, Faculty of Economics and Administrative Sciences, Giresun University, 28200, Giresun, Turkey

    Ufuk Yolcu

Authors
  1. Erol Egrioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ufuk Yolcu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eren Bas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erol Egrioglu.

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

Egrioglu, E., Yolcu, U. & Bas, E. Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony. Granul. Comput. 4, 639–654 (2019). https://doi.org/10.1007/s41066-018-00143-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-018-00143-5

Keywords

Search

Navigation