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JACIII Vol.23 No.6 pp. 1027-1043
doi: 10.20965/jaciii.2019.p1027
(2019)

Paper:

Noise Reduction with Fuzzy Inference Based on Generalized Mean and Singleton Input–Output Rules: Toward Fuzzy Rule Learning in a Unified Inference Platform

Kiyohiko Uehara* and Kaoru Hirota**

*Ibaraki University
4-12-1 Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan
5 South Zhongguancun Street, Haidian District, Beijing 100081, China

Received:
February 28, 2019
Accepted:
July 5, 2019
Published:
November 20, 2019
Keywords:
fuzzy inference, noise reduction, fuzzy rule interpolation, generalized mean, fuzzy rule learning
Abstract

A method is proposed for reducing noise in learning data based on fuzzy inference methods called α-GEMII (α-level-set and generalized-mean-based inference with the proof of two-sided symmetry of consequences) and α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is particularly effective for reducing noise in randomly sampled data given by singleton input–output pairs for fuzzy rule optimization. In the proposed method, α-GEMII and α-GEMINAS are performed with singleton input–output rules and facts defined by fuzzy sets (non-singletons). The rules are initially set by directly using the input–output pairs of the learning data. They are arranged with the facts and consequences deduced by α-GEMII and α-GEMINAS. This process reduces noise to some extent and transforms the randomly sampled data into regularly sampled data for iteratively reducing noise at a later stage. The width of the regular sampling interval can be determined with tolerance so as to satisfy application-specific requirements. Then, the singleton input–output rules are updated with consequences obtained in iteratively performing α-GEMINAS for noise reduction. The noise reduction in each iteration is a deterministic process, and thus the proposed method is expected to improve the noise robustness in fuzzy rule optimization, relying less on trial-and-error-based progress. Simulation results demonstrate that noise is properly reduced in each iteration and the deviation in the learning data is suppressed considerably.

Cite this article as:
K. Uehara and K. Hirota, “Noise Reduction with Fuzzy Inference Based on Generalized Mean and Singleton Input–Output Rules: Toward Fuzzy Rule Learning in a Unified Inference Platform,” J. Adv. Comput. Intell. Intell. Inform., Vol.23, No.6, pp. 1027-1043, 2019.
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References
  1. [1] K. Uehara and K. Hirota, “Noise reduction with inference based on fuzzy rule interpolation at an infinite number of activating points: Toward fuzzy rule learning in a unified inference platform,” J. Adv. Comput. Intell. Intell. Inform., Vol.22, No.6, pp. 883-899, 2018.
  2. [2] K. Uehara and K. Hirota, “Noise reduction with inference based on fuzzy rule interpolation at an infinite number of activating points: A feasibility study,” Proc. of the 5th Int. Workshop on Advanced Computational Intelligence and Intelligent Informatics (IWACIII 2017), AS3-1-2, pp. 1-8, 2017.
  3. [3] K. Uehara and K. Hirota, “Inference with fuzzy rule interpolation at an infinite number of activating points,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.1, pp. 74-90, 2015.
  4. [4] K. Uehara and K. Hirota, “Multi-level control of fuzzy-constraint propagation in inference with fuzzy rule interpolation at an infinite number of activating points,” J. Adv. Comput. Intell. Intell. Inform., Vol.21, No.3, pp. 425-447, 2017.
  5. [5] L. T. Kóczy and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” Int. J. Approx. Reason., Vol.9, No.3, pp. 197-225, 1993.
  6. [6] L. T. Kóczy and K. Hirota, “Size reduction by interpolation in fuzzy rule bases,” IEEE Trans. Syst., Man, Cybern. B (Cybern.), Vol.27, No.1, pp. 14-25, 1997.
  7. [7] D. Tikk and P. Baranyi, “Comprehensive analysis of a new fuzzy rule interpolation method,” IEEE Trans. Fuzzy Syst., Vol.8, No.3, pp. 281-296, 2000.
  8. [8] P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A generalized concept for fuzzy rule interpolation,” IEEE Trans. Fuzzy Syst., Vol.12, No.6, pp. 820-837, 2004.
  9. [9] K. W. Wong, D. Tikk, T. D. Gedeon, and L. T. Kóczy, “Fuzzy rule interpolation for multidimensional input spaces with applications: A case study,” IEEE Trans. Fuzzy Syst., Vol.13, No.6, pp. 809-819, 2005.
  10. [10] Z. Huang and Q. Shen, “Fuzzy interpolative reasoning via scale and move transformations,” IEEE Trans. Fuzzy Syst., Vol.14, No.2, pp. 340-359, 2006.
  11. [11] Z. Huang and Q. Shen, “Fuzzy interpolation and extrapolation: A practical approach,” IEEE Trans. Fuzzy Syst., Vol.16, No.1, pp. 13-28, 2008.
  12. [12] L. T. Kóczy and S. Kovács, “On the preservation of convexity and piecewise linearity in linear fuzzy rule interpolation,” Technical Report, LIFE Chair of Fuzzy Theory, DSS, Tokyo Institute of Technology, Japan, p. 23, 1993.
  13. [13] L. T. Kóczy and S. Kovács, “Shape of the fuzzy conclusion generated by linear interpolation of trapezoidal if ... then rules,” Fuzzy Set Theory and its Applications, Tatra Mountains Mathematical Publications, Mathematical Institute Slovak Academy of Science, Vol.6, pp. 83-93, Bratislava, Slovakia, 1995.
  14. [14] D. Tikk, Z. C. Johanyák, S. Kovács, and K. W. Wong, “Fuzzy rule interpolation and extrapolation techniques: Criteria and evaluation guidelines,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 254-263, 2011.
  15. [15] Q. Shen and L. Yang, “Generalization of scale and move transformation-based fuzzy interpolation,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 288-298, 2011.
  16. [16] L. Kovács, “Compound distance function for similarity measurement between fuzzy sets,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 299-303, 2011.
  17. [17] S. Kato and K. W. Wong, “Intelligent automated guided vehicle controller with reverse strategy,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 304-312, 2011.
  18. [18] D. Vincze and S. Kovács, “Performance optimization of the fuzzy rule interpolation method “FIVE”,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 313-320, 2011.
  19. [19] S. Jin, R. Diao, C. Quek, and Q. Shen, “Backward fuzzy rule interpolation,” IEEE Trans. Fuzzy Syst., Vol.22, No.6, pp. 1682-1698, 2014.
  20. [20] S.-M. Chen and Z.-J. Chen, “Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets,” Information Sciences, Vol.329, pp. 503-523, 2016.
  21. [21] C. Chen, N. M. Parthaláin, Y. Li, C. Price, C. Quek, and Q. Shen, “Rough-fuzzy rule interpolation,” Information Sciences, Vol.351, pp. 1-17, 2016.
  22. [22] Y. Tan, J. Li, M. Wonders, F. Chao, H. P. H. Shum, and L. Yang, “Towards sparse rule base generation for fuzzy rule interpolation,” Proc. of 2016 IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE 2016), pp. 110-117, 2016.
  23. [23] D. Vincze, “Fuzzy rule interpolation and reinforcement learning,” Proc. of 2017 IEEE 15th Int. Symp. on Applied Machine Intelligence and Informatics (SAMI 2017), pp. 173-178, 2017.
  24. [24] L. Yang, F. Chao, and Q. Shen, “Generalized adaptive fuzzy rule interpolation,” IEEE Trans. Fuzzy Syst., Vol.25, No.4, pp. 839-853, 2017.
  25. [25] K. Uehara and K. Hirota, “Noise reduction with fuzzy inference based on generalized mean and singleton input–output rules: A feasibility study,” The 8th Int. Symp. on Computational Intelligence and Industrial Applications (ISCIIA 2018), The 12th China-Japan Int. Workshop on Information Technology and Control Applications (ITCA 2018), 4A1-2-1, pp. 1-8, 2018.
  26. [26] K. Uehara, T. Koyama, and K. Hirota, “Fuzzy inference with schemes for guaranteeing convexity and symmetricity in consequences based on α-cuts,” J. Adv. Comput. Intell. Intell. Inform., Vol.13, No.2, pp. 135-149, 2009.
  27. [27] K. Uehara, T. Koyama, and K. Hirota, “Inference with governing schemes for propagation of fuzzy convex constraints based on α-cuts,” J. Adv. Comput. Intell. Intell. Inform., Vol.13, No.3, pp. 321-330, 2009.
  28. [28] K. Uehara and K. Hirota, “Multi-level control of fuzzy-constraint propagation in inference based on α-cuts and generalized mean,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.4, pp. 647-662, 2013.
  29. [29] K. Uehara and K. Hirota, “Multi-level control of fuzzy-constraint propagation via evaluations with linguistic truth values in generalized-mean-based inference,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.2, pp. 355-377, 2016.
  30. [30] A. Kaufmann, “Introduction to the theory of fuzzy subsets, Vol.1,” Academic Press, pp. 8-30, 1975.
  31. [31] N. R. Pal and J. C. Bezdek, “Measuring fuzzy uncertainty,” IEEE Trans. Fuzzy Syst., Vol.2, No.2, pp. 107-118, 1994.
  32. [32] R. R. Yager, “On the specificity of a possibility distribution,” Fuzzy Sets Syst., Vol.50, No.3, pp. 279-292, 1992.
  33. [33] R. R. Yager, “Measuring tranquility and anxiety in decision making: An application of fuzzy sets,” Int. J. General Systems, Vol.8, No.3, pp. 139-146, 1982.
  34. [34] L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst. Man Cybern., Vol.SMC-3, No.1, pp. 28-44, 1973.
  35. [35] V. Ravi, D. Pradeepkumar, and K. Deb, “Financial time series prediction using hybrids of chaos theory, multi-layer perceptron and multi-objective evolutionary algorithms,” Swarm and Evolutionary Computation, Vol.36, pp. 136-149, 2017.
  36. [36] N. V. Truc and D. T. Anh, “Chaotic time series prediction using radial basis function networks,” Proc. 2018 4th Int. Conf. on Green Technology and Sustainable Development (GTSD), pp. 753-758, 2018.
  37. [37] M. Das and S. K. Ghosh, “Data-driven approaches for meteorological time series prediction: A comparative study of the state-of-the-art computational intelligence techniques,” Pattern Recognition Letters, Vol.105, pp. 155-164, 2018.
  38. [38] M. Han, K. Zhong, T. Qiu, and B. Han, “Interval type-2 fuzzy neural networks for chaotic time series prediction: A concise overview,” IEEE Trans. Cybern., Vol.49, No.7, pp. 2720-2731, 2019.
  39. [39] P. Jiang, B. Wang, H. Li, and H. Lu “Modeling for chaotic time series based on linear and nonlinear framework: Application to wind speed forecasting,” Energy, Vol.173, pp. 468-482, 2019.
  40. [40] R. Ak, O. Fink, and E. Zio, “Two machine learning approaches for short-term wind speed time-series prediction,” IEEE Trans. Neural Networks and Learning Systems, Vol.27, No.8, pp. 1734-1747, 2016.

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Last updated on Nov. 26, 2020