Abstract
This paper introduces an adaptive interval fuzzy modeling method using participatory learning and interval-valued stream data. The model is a collection of fuzzy functional rules in which the rule base structure and the parameters of the rules evolve simultaneously as data are input. The evolving nature of the method allows continuous model adaptation using the stream interval input data. The method employs participatory learning to cluster the interval input data recursively, constructs a fuzzy rule for each cluster, uses the weighted recursive least squares to update the parameters of the rule consequent intervals, and returns an interval-valued output. The method is evaluated using actual data to model and forecast the daily lowest and highest prices of the four most traded cryptocurrencies, BitCoin, Ethereum, XRP, and LiteCoin. The performance of the adaptive interval fuzzy modeling is compared with the adaptive neuro-fuzzy inference system, long short-term memory neural network, autoregressive integrated moving average, exponential smoothing state model, and the naïve random walk methods. Results show that the suggested interval fuzzy model outperforms all these methods in predicting prices in the digital coin market, especially when considering directional accuracy measure.


Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.Notes
Selection is made one choosing cryptocurrencies with the highest liquidity and market capitalization. The data are available at https://coinmarketcap.com/.
Examples of the fuzzy rules are not shown. They are available upon request.
References
Angelov P (2010) Evolving Takagi–Sugeno fuzzy systems from data streams (eTS+). In: Angelov P, Filev D, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley and IEEE Press, Hoboken, pp 21–50
Angelov P, Filev D (2004) An approach to online identification of Takagi–Sugeno fuzzy models. IEEE Trans Syst Man Cybern B 34(1):484–498
Arroyo J, Espínola R, Maté C (2011) Different approaches to forecast interval time series: a comparison in finance. Comput Econ 27(2):169–191
Billard L, Diday E (2000) Regression analysis for interval-valued data. In: Data analysis, classification and related methods: proceedings of the 7th conference of the IFCS, pp 369–374
Burns K, Moosa I (2015) Enhancing the forecasting power of exchange rate models by introducing nonlinearity: does it work? Econ Model 50:27–39
Corbet S, Meegan A, Larkin C, Lucey B, Yarovaya L (2018) Exploring the dynamic relationships between cryptocurrencies and other financial assets. Econ Lett 165:28–34
Fagundes R, De Souza R, Cysneiros F (2014) Interval kernel regression. Neurocomputing 128:371–388
Froelich W, Salmeron J (2014) Evolutionary learning of fuzzy grey cognitive maps for the forecasting of multivariate, interval-valued time series. Int J Approx Reason 55:1319–1335
Hajek P, Froelich W, Prochazka F (2020) Intuitionistic fuzzy grey cognitive maps for forecasting interval-valued time series. Neurocomputing 400:173–185
Hamilton J (1994) Time series analysis. Princeton University Press, Princeton
Huttenlocher D, Klanderman G, Rucklidge W (1993) Comparing images using the Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 15(9):850–863
Hyndman R, Koehler A, Ord J, Snyder R (2008) Forecasting with exponential smoothing: the state space approach. Springer, Berlin
Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685
Li B, Shen Y, Li B (2008) A new algorithm for computing the minimum Hausdorff distance between two point sets on a line under translation. Inf Process Lett 106(2):52–58
Lim C (2016) Interval-valued data regression using nonparametric additive models. J Korean Stat Soc 45(3):358–370
Lima Neto E, de Carvalho F (2010) Constrained linear regression models for symbolic interval-valued variables. Comput Stat Data Anal 54(2):333–347
Ljung L (1988) System identification: theory for the user. Prentice-Hall, Englewood Cliffs
Maciel L, Ballini R, Gomide F, Yager RR (2016) Participatory learning fuzzy clustering for interval-valued data. In: Proceedings of the 16th international conference on information processing and management of uncertainty in knowledge-based systems (IPMU 2016). Eindhoven, pp 1–8
Maciel L, Gomide F, Ballini R (2015) Evolving possibilistic fuzzy modeling for financial interval time series forecasting. In: Proceedings of annual conference on North American fuzzy information processing society (NAFIPS) held jointly 5th world conference on soft computing (WConSC), pp 1–6
Maia A, de Carvalho F (2011) Holt’s exponential smoothing and neural network models for forecasting interval-valued time series. Int J Forecast 27(3):740–759
Maia A, de Carvalho F, Ludermir T (2008) Forecasting models for interval-valued time series. Neurocomputing 71(16–18):3344–3352
Meese R, Rogoff K (1983) Empirical exchange rate models of the seventies: do they fit out of sample? J Int Econ 14(1–2):3–24
Moore R, Kearfott R, Cloud M (2009) Introduction to interval analysis. SIAM Press, Philadelphia
Moosa I, Burns K (2014) The unbeatable random walk in exchange rate forecasting: reality or myth? J Macroecon 40:69–81
Rodrigues P, Salish N (2015) Modeling and forecasting interval time series with threshold models. Adv Data Anal Class 9(1):41–57
Roque A, Maté C, Arroyo J, Sarabia A (2007) iMLP: applying multi-layer perceptrons to interval-valued data. Neural Process Lett 25(2):157–169
Silva L, Gomide F, Yager R (2005) Participatory learning in fuzzy clustering. In: IEEE International conference on fuzzy systems, Reno, pp 857–861
Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Set Syst 161:1564–1584
Sun Y, Han A, Hong Y, Wang S (2018) Threshold autoregressive models for interval-valued time series data. J Econom 206:414–446
Sun Y, Zhang X, Hong Y, Wang S (2018) Asymmetric pass-through of oil prices to gasoline prices with interval time series modelling. Energy Econ 78:165–173
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern SMC–15(1):116–132
Tao X, Li C, Bao Y, Hu Z, Lu Z (2015) A combination method for interval forecasting of agricultural commodity futures prices. Knowl Based Syst 77:92–102
Wang X, Li S (2011) The interval autoregressive time series model. In: Proceedings IEEE international conference fuzzy system (FUZZ-IEEE), pp 2528–2533
Xiong T, Bao Y, Hu Z (2014) Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting. Knowl Based Syst 55:87–100
Acknowledgements
The authors are grateful to the Brazilian National Council for Scientific and Technological Development (CNPq) for Grants 304456/2020-9 (Leandro Maciel) and 302467/2019-0 (Fernando Gomide). The comments and suggestions of the reviewers are also kindly acknowledged.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Maciel, L., Ballini, R. & Gomide, F. Adaptive fuzzy modeling of interval-valued stream data and application in cryptocurrencies prediction. Neural Comput & Applic 35, 7149–7159 (2023). https://doi.org/10.1007/s00521-021-06263-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-06263-5