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Time-Series Forecasting via Complex Fuzzy Logic

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Frontiers of Higher Order Fuzzy Sets

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.

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References

  1. D. Ramot et al., Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)

    Article  Google Scholar 

  2. Z. Chen et al., ANCFIS: A neurofuzzy architecture employing complex fuzzy sets. IEEE Trans. Fuzzy Syst. 19(2), 305–322 (2011)

    Article  Google Scholar 

  3. 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

    Google Scholar 

  4. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis. Cambridge Nonlinear Science Series, vol. xvi (Cambridge University Press, Cambridge, 1997), p. 304

    Google Scholar 

  5. 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

    Google Scholar 

  6. D. Ramot et al., Complex fuzzy logic. IEEE Trans. Fuzzy Syst. 11(4), 450–461 (2003)

    Article  Google Scholar 

  7. S. Dick, Toward complex fuzzy logic. IEEE Trans. Fuzzy Syst. 13(3), 405–414 (2005)

    Article  Google Scholar 

  8. D.E. Tamir, L. Jin, A. Kandel, A new interpretation of complex membership grade. Int. J. Intelli. Syst. 26(4), 285–312 (2011)

    Article  MATH  Google Scholar 

  9. D.E. Tamir, A. Kandel, Axiomatic theory of complex fuzzy logic and complex fuzzy classes. Int. J. Comp. Commun. Control VI(3), (2011)

    Google Scholar 

  10. L. Běhounek, P. Cintula, Fuzzy class theory. Fuzzy Set. Syst. 154(1), 34–55 (2005)

    Article  MATH  Google Scholar 

  11. 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

    Google Scholar 

  12. D.E. Tamir et al., Discrete complex fuzzy logic, in Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American, IEEE, 2012

    Google Scholar 

  13. S.D. Zenzo, A many-valued logic for approximate reasoning. IBM J. Res. Dev. 32(4), 552–565 (1988)

    Article  Google Scholar 

  14. A.R. Salleh, Complex intuitionistic fuzzy sets, in AIP Conference Proceedings, 2012

    Google Scholar 

  15. K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Set. Syst. 20(1), 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  16. R.R. Yager, A.M. Abbasov, Pythagorean membership grades, complex numbers, and decision making. Int. J. intell. Syst. 28, 436–452 (2013)

    Article  Google Scholar 

  17. G. Zhang et al., Operation properties and δ-equalities of complex fuzzy sets. Int. J. Approx. Reason. 50(8), 1227–1249 (2009)

    Article  MATH  Google Scholar 

  18. 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

    Google Scholar 

  19. A.U.M. Alkouri, A.R. Salleh, Complex Atanassov’s intuitionistic Fuzzy relation, in Abstract and Applied Analysis (Hindawi Publishing Corporation, Nasr City, 2013)

    Google Scholar 

  20. 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

    Google Scholar 

  21. 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

    Google Scholar 

  22. 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

    Google Scholar 

  23. A. Hirose, Complex-Valued Neural Networks, vol. 400 (Springer, Berlin, 2012)

    Book  MATH  Google Scholar 

  24. H.E. Michel, A.A.S. Awwal, Artificial neural networks using complex numbers and phase encoded weights. Appl. Opt. 49(10), B71–B82 (2010)

    Article  Google Scholar 

  25. A.J. Noest, Discrete-state phasor neural networks. Phys. Rev. A 38(4), 2196 (1988)

    Article  Google Scholar 

  26. 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

    Google Scholar 

  27. 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

    Google Scholar 

  28. A. Malekzadeh-A, M.-R. Akbarzadeh-T, Complex-valued adaptive neuro fuzzy inference system-CANFIS. Proc. World Aut. Congr. 17, 477–482 (2004)

    Google Scholar 

  29. S. Aghakhani, S. Dick, An on-line learning algorithm for complex fuzzy logic, in Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, IEEE, 2010

    Google Scholar 

  30. 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)

    Article  Google Scholar 

  31. 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

    Google Scholar 

  32. 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)

    Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. 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)

    MATH  MathSciNet  Google Scholar 

  35. 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

    Google Scholar 

  36. 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)

    Google Scholar 

  37. 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)

    Google Scholar 

  38. H. Sun, S. Wang, Q. Jiang, FCM-based model selection algorithms for determining the number of clusters. Pattern Recogn. 37(10), 2027–2037 (2004)

    Article  MATH  Google Scholar 

  39. 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)

    Article  Google Scholar 

  40. 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)

    Google Scholar 

  41. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I. Inform. Sci. 8(3), 199–249 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  42. A. Deshmukh et al., Implementation of complex fuzzy logic modules with VLSI approach. Int. J. Comp. Sci. Netw. Security 8, 172–178 (2008)

    MathSciNet  Google Scholar 

  43. R. Hegger, H. Kantz, T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9(2), 413–435 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  44. 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)

    Article  Google Scholar 

  45. NREL Staff, Lowry Range Solar Station (LRSS), Colarado State Land Board, http://www.nrel.gov/midc/lrss

  46. A. Bellini et al., Simplified model of a photovoltaic module, in Applied Electronics, 2009. AE 2009, IEEE, 2009

    Google Scholar 

  47. J.S.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cyb. 23(3), 665–685 (1993)

    Article  Google Scholar 

  48. M. Li et al., Sunspot numbers forecasting using neural networks, in Intelligent Control, 1990. Proceedings., 5th IEEE International Symposium on, IEEE, 1990

    Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Alberta, 2nd Floor ECERF Building, 9107–116 Street, T6G 2V4, Edmonton, AB, Canada

    Omolbanin Yazdanbakhsh & Dr. Scott Dick

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  1. Omolbanin Yazdanbakhsh
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  2. Dr. Scott Dick
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Correspondence to Scott Dick .

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Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Alireza Sadeghian

  2. Ryerson University, Toronto, Ontario, Canada

    Hooman Tahayori

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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

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  • DOI: https://doi.org/10.1007/978-1-4614-3442-9_8

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