Neurofuzzy Systems

Chapter

Abstract

The neurofuzzy system is inspired by the biological-cognitive synergism in human intelligence. It is the synergism between the neuronal transduction/processing of sensory signals, and the corresponding cognitive, perceptual, and linguistic functions of the brain.

References

  1. 1.
    Abe, S., & Lan, M. S. (1995). Fuzzy rules extraction directly from numerical data for function approximation. IEEE Transactions on Systems, Man, and Cybernetics, 25(1), 119–129.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Angulo, C., Anguita, D., Gonzalez-Abril, L., & Ortega, J. A. (2008). Support vector machines for interval discriminant analysis. Neurocomputing, 71, 1220–1229.CrossRefGoogle Scholar
  3. 3.
    Azeem, M. F., Hanmandlu, M., & Ahmad, N. (2000). Generalization of adaptive neuro-fuzzy inference systems. IEEE Transactions on Neural Networks, 11(6), 1332–1346.CrossRefGoogle Scholar
  4. 4.
    Baker, M. R., & Patil, R. B. (1998). Universal approximation theorem for interval neural networks. Reliable Computing, 4, 235–239.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Barakat, N. H., & Bradley, A. P. (2007). Rule extraction from support vector machines: A sequential covering approach. IEEE Transactions on Knowledge and Data Engineering, 19(6), 729–741.CrossRefGoogle Scholar
  6. 6.
    Batuwita, R., & Palade, V. (2010). FSVM-CIL: Fuzzy support vector machines for class imbalance learning. IEEE Transactions on Fuzzy Systems, 18(3), 558–571.CrossRefGoogle Scholar
  7. 7.
    Benitez, J. M., Castro, J. L., & Requena, I. (1997). Are artificial neural networks black boxes? IEEE Transactions on Neural Networks, 8(5), 1156–1164.CrossRefGoogle Scholar
  8. 8.
    Berenji, H. R., & Vengerov, D. (2003). A convergent actor-critic-based FRL algorithm with application to power management of wireless transmitters. IEEE Transactions on Fuzzy Systems, 11(4), 478–485.CrossRefGoogle Scholar
  9. 9.
    Castro, J. L., Mantas, C. J., & Benitez, J. M. (2002). Interpretation of artificial neural networks by means of fuzzy rules. IEEE Transactions on Neural Networks, 13(1), 101–116.CrossRefGoogle Scholar
  10. 10.
    Castro, J. L., Flores-Hidalgo, L. D., Mantas, C. J., & Puche, J. M. (2007). Extraction of fuzzy rules from support vector machines. Fuzzy Sets and Systems, 158, 2057–2077.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Cechin, A., Epperlein, U., Koppenhoefer, B., & Rosenstiel, W. (1996). The extraction of Sugeno fuzzy rules from neural networks. In M. Verleysen (Ed.), Proceedings of the European Symposium on Artificial Neural Networks (pp. 49–54). Bruges, Belgium.Google Scholar
  12. 12.
    Chen, M. S., & Liou, R. J. (1999). An efficient learning method of fuzzy inference system. In Proceedings of IEEE International Fuzzy Systems Conference (pp. 634–638). Seoul, Korea.Google Scholar
  13. 13.
    Chen, Z.-P., Jiang, J.-H., Li, Y., Liang, Y.-Z., & Yu, R.-Q. (1999). Fuzzy linear discriminant analysis for chemical datasets. Chemometrics and Intelligent Laboratory Systems, 45, 295–302.CrossRefGoogle Scholar
  14. 14.
    Chen, J. L., & Chang, J. Y. (2000). Fuzzy perceptron neural networks for classifiers with numerical data and linguistic rules as inputs. IEEE Transactions on Fuzzy Systems, 8(6), 730–745.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Chen, J.-H., & Chen, C.-S. (2002). Fuzzy kernel perceptron. IEEE Transactions on Neural Networks, 13(6), 1364–1373.CrossRefGoogle Scholar
  16. 16.
    Chen, D., He, Q., & Wang, X. (2010). FRSVMs: Fuzzy rough set based support vector machines. Fuzzy Sets and Systems, 161, 596–607.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Chiang, J. H., & Hao, P. Y. (2004). Support vector learning mechanism for fuzzy rule-based modeling: A new approach. IEEE Transactions on Fuzzy Systems, 12(1), 1–12.CrossRefGoogle Scholar
  18. 18.
    Chuang, C.-C. (2007). Fuzzy weighted support vector regression with a fuzzy partition. IEEE Transactions on Systems, Man, and Cybernetics Part B, 37(3), 630–640.CrossRefGoogle Scholar
  19. 19.
    Denoeux, T., & Masson, M. H. (2004). Principal component analysis of fuzzy data using autoassociative neural networks. IEEE Transactions on Fuzzy Systems, 12(3), 336–349.CrossRefGoogle Scholar
  20. 20.
    Derhami, V., Majd, V. J., & Ahmadabadi, M. N. (2008). Fuzzy Sarsa learning and the proof of existence of its stationary points. Asian Journal of Control, 10(5), 535–549.Google Scholar
  21. 21.
    Derhami, V., Majd, V. J., & Ahmadabadi, M. N. (2010). Exploration and exploitation balance management in fuzzy reinforcement learning. Fuzzy Sets and Systems, 161, 578–595.CrossRefMathSciNetGoogle Scholar
  22. 22.
    Duch, W. (2005). Uncertainty of data, fuzzy membership functions, and multilayer perceptrons. IEEE Transactions on Neural Networks, 16(1), 10–23.CrossRefGoogle Scholar
  23. 23.
    Fung, G., Sandilya, S., & Rao, R. (2005). Rule extraction from linear support vector machines. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining (KDD) (pp. 32–40).Google Scholar
  24. 24.
    Gabrays, B., & Bargiela, A. (2000). General fuzzy min-max neural networks for clustering and classification. IEEE Transactions on Neural Networks, 11(3), 769–783.CrossRefGoogle Scholar
  25. 25.
    Gallant, S. I. (1988). Connectionist expert systems. Communications of the ACM, 31(2), 152–169.CrossRefGoogle Scholar
  26. 26.
    Guillaume, S. (2001). Designing fuzzy inference systems from data: An interpretability-oriented review. IEEE Transactions on Fuzzy Systems, 9(3), 426–443.CrossRefMathSciNetGoogle Scholar
  27. 27.
    Hao, P.-Y. (2008). Fuzzy one-class support vector machines. Fuzzy Sets and Systems, 159, 2317–2336.CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Hayashi, Y., Buckley, J. J., & Czogala, E. (1993). Fuzzy neural network with fuzzy signals and weights. International Journal of Intelligent Systems, 8(4), 527–537.CrossRefMATHGoogle Scholar
  29. 29.
    Ho, D. W. C., Zhang, P. A., & Xu, J. (2001). Fuzzy wavelet networks for function learning. IEEE Transactions on Fuzzy Systems, 9(1), 200–211.CrossRefGoogle Scholar
  30. 30.
    Honda, K., Ichihashi, H., Ohue, M., & Kitaguchi, K. (2000). Extraction of local independent components using fuzzy clustering. In Proceedings of 6th International Conference on Soft Computing (IIZUKA2000) (pp. 837–842).Google Scholar
  31. 31.
    Hwang, C., Hong, D. H., & Seok, K. H. (2006). Support vector interval regression machine for crisp input and output data. Fuzzy Sets and Systems, 157, 1114–1125.CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    Ishikawa, M. (2000). Rule extraction by successive regularization. Neural Networks, 13(10), 1171–1183.CrossRefGoogle Scholar
  33. 33.
    Ishibuchi, H., Tanaka, H., & Okada, H. (1993). An architecture of neural networks with interval weights and its application to fuzzy regression analysis. Fuzzy Sets and Systems, 57, 27–39.CrossRefMATHMathSciNetGoogle Scholar
  34. 34.
    Jacobsson, H. (2005). Rule extraction from recurrent neural networks: A taxonomy and review. Neural Computation, 17(6), 1223–1263.Google Scholar
  35. 35.
    Jang, J. S. R., & Sun, C. I. (1993). Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Transactions on Neural Networks, 4(1), 156–159.Google Scholar
  36. 36.
    Jang, J. S. R. (1993). ANFIS: Adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685.CrossRefGoogle Scholar
  37. 37.
    Jang, J. S. R., & Mizutani, E. (1996). Levenberg-Marquardt method for ANFIS learning. In Proceedings of Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS) (pp. 87–91). Berkeley, CA.Google Scholar
  38. 38.
    Jang, J. S. R., & Sun, C. I. (1995). Neuro-fuzzy modeling and control. Proceedings of the IEEE, 83(3), 378–406.Google Scholar
  39. 39.
    Jeng, J.-T., & Lee, T.-T. (1999). Support vector machines for the fuzzy neural networks. In Proceedings of IEEE International Conference on Systems, Man, and Cybernetics (pp. 115–120).Google Scholar
  40. 40.
    Jeng, J.-T., Chuang, C.-C., & Su, S.-F. (2003). Support vector interval regression networks for interval regression analysis. Fuzzy Sets and Systems, 138, 283–300.CrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    Jin, Y. (2003). Advanced fuzzy systems design and applications. Heidelberg: Physica-Verlag.Google Scholar
  42. 42.
    Jouffe, L. (1998). Fuzzy inference system learning by reinforcement methods. IEEE Transactions on Systems, Man, and Cybernetics Part C, 28(3), 338–355.CrossRefGoogle Scholar
  43. 43.
    Juang, C.-F., Chiu, S.-H., & Chang, S.-W. (2007). A self-organizing TS-type fuzzy network with support vector learning and its application to classification problems. IEEE Transactions on Fuzzy Systems, 15(5), 998–1008.CrossRefGoogle Scholar
  44. 44.
    Juang, C.-F., & Hsieh, C.-D. (2009). TS-fuzzy system-based support vector regression. Fuzzy Sets and Systems, 160, 2486–2504.CrossRefMATHMathSciNetGoogle Scholar
  45. 45.
    Keller, J. M., Gray, M. R., & Givens, J. A, Jr. (1985). A fuzzy \(K\)-nearest neighbor algorithm. IEEE Transactions on Systems, Man, and Cybernetics, 15(4), 580–585.CrossRefGoogle Scholar
  46. 46.
    Kim, J., & Kasabov, N. (1999). HyFIS: Adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Networks, 12, 1301–1319.CrossRefGoogle Scholar
  47. 47.
    Kolman, E., & Margaliot, M. (2005). Are artificial neural networks white boxes? IEEE Transactions on Neural Networks, 16(4), 844–852.CrossRefGoogle Scholar
  48. 48.
    Kolman, E., & Margaliot, M. (2009). Extracting symbolic knowledge from recurrent neural networks: A fuzzy logic approach. Fuzzy Sets and Systems, 160, 145–161.CrossRefMATHMathSciNetGoogle Scholar
  49. 49.
    Kwak, K. C., & Pedry, W. (2005). Face recognition using a fuzzy fisher classifier. Pattern Recognition, 38(10), 1717–1732.CrossRefGoogle Scholar
  50. 50.
    Lin, C.-F., & Wang, S.-D. (2002). Fuzzy support vector machines. IEEE Transactions on Neural Networks, 13(2), 464–471.CrossRefGoogle Scholar
  51. 51.
    Lin, C.-T., Yeh, C.-M., Liang, S.-F., Chung, J.-F., & Kumar, N. (2006). Support-vector-based fuzzy neural network for pattern classification. IEEE Transactions on Fuzzy Systems, 14(1), 31–41.CrossRefGoogle Scholar
  52. 52.
    Liu, P. (2000). Max-min fuzzy Hopfield neural networks and an efficient learning algorithm. Fuzzy Sets and Systems, 112, 41–49.CrossRefMATHMathSciNetGoogle Scholar
  53. 53.
    Liu, P., & Li, H. (2004). Efficient learning algorithms for three-layer regular feedforward fuzzy neural networks. IEEE Transactions on Neural Networks, 15(3), 545–558.Google Scholar
  54. 54.
    Liu, P., & Li, H. (2005). Hierarchical TS fuzzy system and its universal approximation. Information Sciences, 169, 279–303.CrossRefMATHMathSciNetGoogle Scholar
  55. 55.
    Liu, Y.-H., & Chen, Y.-T. (2007). Face recognition using total margin-based adaptive fuzzy support vector machines. IEEE Transactions on Neural Networks, 18(1), 178–192.CrossRefGoogle Scholar
  56. 56.
    Lou, S. T., & Zhang, X. D. (2003). Fuzzy-based learning rate determination for blind source separation. IEEE Transactions on Fuzzy Systems, 11(3), 375–383.CrossRefGoogle Scholar
  57. 57.
    Lughofer, E. D. (2008). FLEXFIS: A robust incremental learning approach for evolving Takagi-Sugeno fuzzy models. IEEE Transactions on Fuzzy Systems, 16(6), 1393–1410.CrossRefGoogle Scholar
  58. 58.
    Martens, D., Baesens, B., & Van Gestel, T. (2009). Decompositional rule extraction from support vector machines by active learning. IEEE Transactions on Knowledge and Data Engineering, 21(2), 178–191.CrossRefGoogle Scholar
  59. 59.
    Mitra, S., & Hayashi, Y. (2000). Neuro-fuzzy rule generation: Survey in soft computing framework. IEEE Transactions on Neural Networks, 11(3), 748–768.CrossRefGoogle Scholar
  60. 60.
    Mizutani, E., & Jang, J. S. (1995). Coactive neural fuzzy modeling. In Proceedings of IEEE International Conference on Neural Networks (vol. 2, pp. 760–765). Perth, Australia.Google Scholar
  61. 61.
    Nauck, D., Klawonn, F., & Kruse, R. (1997). Foundations of neuro-fuzzy systems. New York: Wiley.Google Scholar
  62. 62.
    Nicholls, J. G., Martin, A. R., & Wallace, B. G. (1992). From neuron to brain: A cellular and molecular approach to the function of the nervous system (3rd ed.). Sunderland, MA: Sinauer Associates.Google Scholar
  63. 63.
    Nikov, A., & Stoeva, S. (2001). Quick fuzzy backpropagation algorithm. Neural Networks, 14, 231–244.CrossRefGoogle Scholar
  64. 64.
    Nomura, H., Hayashi, I., & Wakami, N. (1992). A learning method of fuzzy inference rules by descent method. In Proceedings of IEEE International Conference on Fuzzy Systems (pp. 203–210). San Diego, CA.Google Scholar
  65. 65.
    Nunez, H., Angulo, C., & Catala, A. (2002). Rule extraction from support vector machines. In Proceedings of the European Symposium on Artificial Neural Networks (pp. 107–112).Google Scholar
  66. 66.
    Nunez, H., Angulo, C., & Catala, A. (2006). Rule-based learning systems for support vector machines. Neural Processing Letters, 24, 1–18.CrossRefGoogle Scholar
  67. 67.
    Omlin, C. W., & Giles, C. L. (1996). Extraction of rules from discrete-time recurrent neural networks. Neural Networks, 9, 41–52.CrossRefGoogle Scholar
  68. 68.
    Omlin, C. W., Thornber, K. K., & Giles, C. L. (1998). Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks. IEEE Transactions on Fuzzy Systems, 6, 76–89.CrossRefGoogle Scholar
  69. 69.
    Pedrycz, W., & Rocha, A. F. (1993). Fuzzy-set based models of neurons and knowledge-based networks. IEEE Transactions on Fuzzy Systems, 1(4), 254–266.CrossRefGoogle Scholar
  70. 70.
    Pedrycz, W., Reformat, M., & Li, K. (2006). OR/AND neurons and the development of interpretable logic models. IEEE Transactions on Neural Networks, 17(3), 636–658.CrossRefGoogle Scholar
  71. 71.
    Rong, H.-J., Sundararajan, N., Huang, G.-B., & Saratchandran, P. (2006). Sequential adaptive fuzzy inference system (SAFIS) for nonlinear system identification and prediction. Fuzzy Sets and Systems, 157, 1260–1275.CrossRefMATHMathSciNetGoogle Scholar
  72. 72.
    Roque, A. M. S., Mate, C., Arroyo, J., & Sarabia, A. (2007). iMLP: Applying multi-layer perceptrons to interval-valued data. Neural Processing Letters, 25, 157–169.CrossRefGoogle Scholar
  73. 73.
    Simpson, P. K. (1992). Fuzzy min-max neural networks-Part I: Classification. IEEE Transactions on Neural Networks, 3, 776–786.CrossRefGoogle Scholar
  74. 74.
    Simpson, P. K. (1993). Fuzzy min-max neural networks-Part II: Clustering. IEEE Transactions on Fuzzy Systems, 1(1), 32–45.CrossRefGoogle Scholar
  75. 75.
    Sisman-Yilmaz, N. A., Alpaslan, F. N., & Jain, L. (2004). ANFIS-unfolded-in-time for multivariate time series forecasting. Neurocomputing, 61, 139–168.CrossRefGoogle Scholar
  76. 76.
    Soria-Olivas, E., Martin-Guerrero, J. D., Camps-Valls, G., Serrano-Lopez, A. J., Calpe-Maravilla, J., & Gomez-Chova, L. (2003). A low-complexity fuzzy activation function for artificial neural networks. IEEE Transactions on Neural Networks, 14(6), 1576–1579.CrossRefGoogle Scholar
  77. 77.
    Stoeva, S., & Nikov, A. (2000). A fuzzy backpropagation algorithm. Fuzzy Sets and Systems, 112, 27–39.CrossRefMATHMathSciNetGoogle Scholar
  78. 78.
    Sun, C. T. (1994). Rule-base structure identification in an adaptive-network-based inference system. IEEE Transactions on Fuzzy Systems, 2(1), 64–79.CrossRefGoogle Scholar
  79. 79.
    Sussner, P., & Valle, M. E. (2006). Implicative fuzzy associative memories. IEEE Transactions on Fuzzy Systems, 14(6), 793–807.CrossRefGoogle Scholar
  80. 80.
    Thawonmas, R., & Abe, S. (1999). Function approximation based on fuzzy rules extracted from partitioned numerical data. IEEE Transactions on Systems, Man, and Cybernetics Part B, 29(4), 525–534.CrossRefGoogle Scholar
  81. 81.
    Tsujinishi, D., & Abe, S. (2003). Fuzzy least squares support vector machines for multiclass problems. Neural Networks, 16, 785–792.CrossRefGoogle Scholar
  82. 82.
    Uehara, K., & Fujise, M. (1993). Fuzzy inference based on families of \(\alpha \)-level sets. IEEE Transactions on Fuzzy Systems, 1(2), 111–124.CrossRefGoogle Scholar
  83. 83.
    Ultsch, A., Mantyk, R., & Halmans, G. (1993). Connectionist knowledge acquisition tool: CONKAT. In D. J. Hand (Ed.), Artificial Intelligence Frontiers in Statistics: AI and Statistics III (pp. 256–263). London: Chapman & Hall.Google Scholar
  84. 84.
    Vuorimaa, P. (1994). Fuzzy self-organizing map. Fuzzy Sets and Systems, 66(2), 223–231.CrossRefGoogle Scholar
  85. 85.
    Wang, L. X., & Mendel, J. M. (1992). Generating fuzzy rules by learning from examples. IEEE Transactions on Systems, Man, and Cybernetics, 22(6), 1414–1427.CrossRefMathSciNetGoogle Scholar
  86. 86.
    Wang, L. X., & Mendel, J. M. (1992). Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Transactions on Neural Networks, 3(5), 807–814.CrossRefGoogle Scholar
  87. 87.
    Wang, L. X. (1999). Analysis and design of hierarchical fuzzy systems. IEEE Transactions on Fuzzy Systems, 7(5), 617–624.CrossRefGoogle Scholar
  88. 88.
    Wang, L. X., & Wei, C. (2000). Approximation accuracy of some neuro-fuzzy approaches. IEEE Transactions on Fuzzy Systems, 8(4), 470–478.CrossRefGoogle Scholar
  89. 89.
    Wu, S., & Er, M. J. (2000). Dynamic fuzzy neural networks: A novel approach to function approximation. IEEE Transactions on Systems, Man, and Cybernetics, 30(2), 358–364.CrossRefGoogle Scholar
  90. 90.
    Yan, H.-S., & Xu, D. (2007). An approach to estimating product design time based on fuzzy \(\nu \)-support vector machine. IEEE Transactions on Neural Networks, 18(3), 721–731.CrossRefMATHMathSciNetGoogle Scholar
  91. 91.
    Yang, W., Yan, X., Zhang, L., & Sun, C. (2010). Feature extraction based on fuzzy 2DLDA. Neurocomputing, 73, 1556–1561.CrossRefGoogle Scholar
  92. 92.
    Yang, X., Zhang, G., Lu, J., & Ma, J. (2011). A kernel fuzzy c-means clustering-based fuzzy support vector machine algorithm for classification problems with outliers or noises. IEEE Transactions on Fuzzy Systems, 19(1), 105–115.CrossRefGoogle Scholar
  93. 93.
    Zhang, D., Bai, X. L., & Cai, K. Y. (2004). Extended neuro-fuzzy models of multilayer perceptrons. Fuzzy Sets and Systems, 142, 221–242.CrossRefMATHMathSciNetGoogle Scholar
  94. 94.
    Zhou, S.-M., & Gan, J. Q. (2007). Constructing L2-SVM-based fuzzy classifiers in high-dimensional space with automatic model selection and fuzzy rule ranking. IEEE Transactions on Fuzzy Systems, 15(3), 398–409.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Enjoyor LabsEnjoyor Inc.HangzhouChina
  2. 2.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

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