Abstract
Adaptive neuro-complex-fuzzy inference system (ANCFIS) is a neuro-fuzzy system that employs complex fuzzy sets for time-series forecasting. One of the particular advantages of this architecture is that each input to the network is a windowed segment of the time series, rather than a single lag as in most other neural networks. This allows ANCFIS to predict even chaotic time series very accurately, using a small number of rules. Some recent findings, however, indicate that published results on ANCFIS are suboptimal; they could be improved by changing how the length of an input window is determined, and/or subsampling the input window.
We compare the performance of ANCFIS using three different approaches to defining an input window, across six time-series datasets. These include chaotic datasets and time series up to 20,000 observations in length. We found that the optimal choice of input formats was dataset dependent, and may be influenced by the size of the dataset. We finally develop a recommended approach to determining input windows that balances the twin concerns of accuracy and computation time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Available online at http://www.ualberta.ca/~yazdanba/SolarData.txt.
References
D. Ramot et al., Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)
Z. Chen et al., ANCFIS: A neurofuzzy architecture employing complex fuzzy sets. IEEE Trans. Fuzzy Syst. 19(2), 305–322 (2011)
C. Li, T.-W. Chiang, Complex neuro-fuzzy self-learning approach to function approximation, in Intelligent Information and Database Systems. (Springer, Berlin, 2010), pp. 289–299
H. Kantz, T. Schreiber, Nonlinear Time Series Analysis. Cambridge Nonlinear Science Series, vol. xvi (Cambridge University Press, Cambridge, 1997), p. 304
O. Yazdanbaksh, A. Krahn, S. Dick, Predicting solar power output using complex fuzzy logic, in IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint, IEEE, 2013
D. Ramot et al., Complex fuzzy logic. IEEE Trans. Fuzzy Syst. 11(4), 450–461 (2003)
S. Dick, Toward complex fuzzy logic. IEEE Trans. Fuzzy Syst. 13(3), 405–414 (2005)
D.E. Tamir, L. Jin, A. Kandel, A new interpretation of complex membership grade. Int. J. Intelli. Syst. 26(4), 285–312 (2011)
D.E. Tamir, A. Kandel, Axiomatic theory of complex fuzzy logic and complex fuzzy classes. Int. J. Comp. Commun. Control VI(3), (2011)
L. Běhounek, P. Cintula, Fuzzy class theory. Fuzzy Set. Syst. 154(1), 34–55 (2005)
D.E. Tamir, M. Last, A. Kandel, The theory and applications of generalized complex fuzzy propositional logic, in Soft Computing: State of the Art Theory and Novel Applications (Springer, Berlin, 2013), pp. 177–192
D.E. Tamir et al., Discrete complex fuzzy logic, in Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American, IEEE, 2012
S.D. Zenzo, A many-valued logic for approximate reasoning. IBM J. Res. Dev. 32(4), 552–565 (1988)
A.R. Salleh, Complex intuitionistic fuzzy sets, in AIP Conference Proceedings, 2012
K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Set. Syst. 20(1), 87–96 (1986)
R.R. Yager, A.M. Abbasov, Pythagorean membership grades, complex numbers, and decision making. Int. J. intell. Syst. 28, 436–452 (2013)
G. Zhang et al., Operation properties and δ-equalities of complex fuzzy sets. Int. J. Approx. Reason. 50(8), 1227–1249 (2009)
G. Zhang et al., Delta-equalities of Complex Fuzzy Relations, in Advanced Information Networking and Applications (AINA), 2010 24th IEEE International Conference on, IEEE, 2010
A.U.M. Alkouri, A.R. Salleh, Complex Atanassov’s intuitionistic Fuzzy relation, in Abstract and Applied Analysis (Hindawi Publishing Corporation, Nasr City, 2013)
D. Moses et al., Linguistic coordinate transformations for complex fuzzy sets, in Fuzzy Systems Conference Proceedings, 1999. FUZZ-IEEE’99. 1999 IEEE International, IEEE, 1999
H.T. Nguyen, A. Kandel, V. Kreinovich, Complex fuzzy sets: towards new foundations, in Fuzzy Systems, 2000. FUZZ IEEE 2000. The Ninth IEEE International Conference on, IEEE, 2000
J. Man, Z. Chen, S. Dick, Towards inductive learning of complex fuzzy inference systems, in Fuzzy Information Processing Society, 2007. NAFIPS’07. Annual Meeting of the North American, IEEE, 2007
A. Hirose, Complex-Valued Neural Networks, vol. 400 (Springer, Berlin, 2012)
H.E. Michel, A.A.S. Awwal, Artificial neural networks using complex numbers and phase encoded weights. Appl. Opt. 49(10), B71–B82 (2010)
A.J. Noest, Discrete-state phasor neural networks. Phys. Rev. A 38(4), 2196 (1988)
I. Nishikawa, T. Iritani, K. Sakakibara, Improvements of the traffic signal control by complex-valued Hopfield networks, in Neural Networks, 2006. IJCNN’06. International Joint Conference on, IEEE, 2006
Y. Li, Y.-T. Jang, Complex adaptive fuzzy inference systems, in Fuzzy Systems Symposium, 1996. ʽSoft Computing in Intelligent Systems and Information Processing’, Proceedings of the 1996 Asian, IEEE, 1996
A. Malekzadeh-A, M.-R. Akbarzadeh-T, Complex-valued adaptive neuro fuzzy inference system-CANFIS. Proc. World Aut. Congr. 17, 477–482 (2004)
S. Aghakhani, S. Dick, An on-line learning algorithm for complex fuzzy logic, in Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, IEEE, 2010
C. Li, T.-W. Chiang, Function approximation with complex neuro-fuzzy system using complex fuzzy sets-a new approach. New Generat. Comput. 29(3), 261–276 (2011)
C. Li, F. Chan, Complex-fuzzy adaptive image restoration-an artificial-bee-colony-based learning approach, in Intelligent Information and Database Systems (Springer, Berlin, 2011), pp. 90–99
Li, C. and F.-T. Chan, Knowledge discovery by an intelligent approach using complex fuzzy sets, in Intelligent Information and Database Systems. Springer, 320–329 (2012)
C. Li, T. Wu, F.-T. Chan, Self-learning complex neuro-fuzzy system with complex fuzzy sets and its application to adaptive image noise canceling. Neurocomputing 94, 121–139 (2012)
C. Li, T.-W. Chiang, Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence. Int. J. Appl. Math. Comp. Sci. 22(4), 787–800 (2012)
C. Li, T.-W. Chiang, Complex fuzzy computing to time series prediction a multi-swarm PSO learning approach, in Intelligent Information and Database Systems (Springer, Berlin, 2011), pp. 242–251
C. Li, T. Chiang, Complex Neurofuzzy ARIMA Forecasting—A New Approach Using Complex Fuzzy Sets, Fuzzy Systems, IEEE Transactions on 21(3), 567–584 (2013)
C. Li, T.-W. Chiang, L.-C. Yeh, A novel self-organizing complex neuro-fuzzy approach to the problem of time series forecasting. Neurocomputing 99, 467–476 (2013)
H. Sun, S. Wang, Q. Jiang, FCM-based model selection algorithms for determining the number of clusters. Pattern Recogn. 37(10), 2027–2037 (2004)
J. Ma, G. Zhang, J. Lu, A method for multiple periodic factor prediction problems using complex fuzzy sets. IEEE Trans. Fuzzy Syst. 20(1), 32–45 (2012)
A.U.M. Alkouri, A.R. Salleh, Linguistic variables, hedges and several distances on complex fuzzy sets. J. Intell. Fuzzy Syst. 26(5), 2527–2535 (2014)
L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I. Inform. Sci. 8(3), 199–249 (1975)
A. Deshmukh et al., Implementation of complex fuzzy logic modules with VLSI approach. Int. J. Comp. Sci. Netw. Security 8, 172–178 (2008)
R. Hegger, H. Kantz, T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9(2), 413–435 (1999)
M.B. Kennel, R. Brown, H.D. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45(6), 3403 (1992)
NREL Staff, Lowry Range Solar Station (LRSS), Colarado State Land Board, http://www.nrel.gov/midc/lrss
A. Bellini et al., Simplified model of a photovoltaic module, in Applied Electronics, 2009. AE 2009, IEEE, 2009
J.S.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cyb. 23(3), 665–685 (1993)
M. Li et al., Sunspot numbers forecasting using neural networks, in Intelligent Control, 1990. Proceedings., 5th IEEE International Symposium on, IEEE, 1990
Acknowledgments
This research was supported in part by the Natural Science and Engineering Research Council of Canada under grant no. RGPIN 262151, and in part by Transport Canada under grant no. RES0017834.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Yazdanbakhsh, O., Dick, S. (2015). Time-Series Forecasting via Complex Fuzzy Logic. In: Sadeghian, A., Tahayori, H. (eds) Frontiers of Higher Order Fuzzy Sets. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3442-9_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-3442-9_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3441-2
Online ISBN: 978-1-4614-3442-9
eBook Packages: EngineeringEngineering (R0)