Abstract
Hybridization of fuzzy logic and neural networks yields neurofuzzy systems, which capture the merits of both paradigms. This chapter first describes how to extract rules from neural networks and data, and then introduces how the synergy of fuzzy logic and neural network paradigms is implemented.
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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.
Angulo, C., Anguita, D., Gonzalez-Abril, L., & Ortega, J. A. (2008). Support vector machines for interval discriminant analysis. Neurocomputing, 71, 1220–1229.
Azeem, M. F., Hanmandlu, M., & Ahmad, N. (2000). Generalization of adaptive neuro-fuzzy inference systems. IEEE Transactions on Neural Networks, 11(6), 1332–1346.
Baker, M. R., & Patil, R. B. (1998). Universal approximation theorem for interval neural networks. Reliable Computing, 4, 235–239.
Batuwita, R., & Palade, V. (2010). FSVM-CIL: Fuzzy support vector machines for class imbalance learning. IEEE Transactions on Fuzzy Systems, 18(3), 558–571.
Benitez, J. M., Castro, J. L., & Requena, I. (1997). Are artificial neural networks black boxes? IEEE Transactions on Neural Networks, 8(5), 1156–1164.
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.
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.
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.
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.
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.
Chen, M. S., & Liou, R. J. (1999). An efficient learning method of fuzzy inference system. In Proceedings of IEEE International Fuzzy Systems (pp. 634–638). Seoul, Korea.
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.
Chen, C. L. P., Zhang, C.-Y., Chen, L., & Gan, M. (2015). Fuzzy restricted Boltzmann machine for the enhancement of deep learning. IEEE Transactions on Fuzzy Systems, 23(6), 2163–2173.
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.
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.
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.
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.
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.
Duch, W. (2005). Uncertainty of data, fuzzy membership functions, and multilayer perceptrons. IEEE Transactions on Neural Networks, 16(1), 10–23.
Feng, S., Chen, C. L. P., & Zhang, C.-Y. (2019). A fuzzy deep model based on fuzzy restricted boltzmann machines for high-dimensional data classification. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2019.2902111 (in press).
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).
Gabrays, B., & Bargiela, A. (2000). General fuzzy min–max neural networks for clustering and classification. IEEE Transactions on Neural Networks, 11(3), 769–783.
Gallant, S. I. (1988). Connectionist expert systems. Communications of the ACM, 31(2), 152–169.
Guillaume, S. (2001). Designing fuzzy inference systems from data: An interpretability-oriented review. IEEE Transactions on Fuzzy Systems, 9(3), 426–443.
Hao, P.-Y. (2008). Fuzzy one-class support vector machines. Fuzzy Sets and Systems, 159, 2317–2336.
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.
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.
Honda, K., Ichihashi, H., Ohue, M., & Kitaguchi, K. (2000). Extraction of local independent components using fuzzy clustering. In Proceedings of the 6th International Conference on Soft Computing (IIZUKA2000) (pp. 837–842).
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.
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.
Ishikawa, M. (2000). Rule extraction by successive regularization. Neural Networks, 13(10), 1171–1183.
Jacobsson, H. (2005). Rule extraction from recurrent neural networks: A taxonomy and review. Neural Computation, 17(6), 1223–1263.
Jang, J. S. R. (1993). ANFIS: Adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685.
Jang, J. S. R., & Mizutani, E. (1996). Levenberg–Marquardt method for ANFIS learning. In Proceedings of Biennial International North American Fuzzy Information Processing (NAFIPS) (pp. 87–91). Berkeley, CA.
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.
Jang, J. S. R., & Sun, C. I. (1995). Neuro-fuzzy modeling and control. Proceedings of the IEEE, 83(3), 378–406.
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.
Jin, Y. (2003). Advanced fuzzy systems design and applications. Heidelberg, Germany: Physica-Verlag.
Jouffe, L. (1998). Fuzzy inference system learning by reinforcement methods. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 28(3), 338–355.
Juang, C.-F., & Hsieh, C.-D. (2009). TS-fuzzy system-based support vector regression. Fuzzy Sets and Systems, 160, 2486–2504.
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.
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.
Kim, J., & Kasabov, N. (1999). HyFIS: Adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Networks, 12, 1301–1319.
Kolman, E., & Margaliot, M. (2005). Are artificial neural networks white boxes? IEEE Transactions on Neural Networks, 16(4), 844–852.
Kolman, E., & Margaliot, M. (2009). Extracting symbolic knowledge from recurrent neural networks—A fuzzy logic approach. Fuzzy Sets and Systems, 160, 145–161.
Lin, C.-F., & Wang, S.-D. (2002). Fuzzy support vector machines. IEEE Transactions on Neural Networks, 13(2), 464–471.
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.
Liu, P. (2000). Max–min fuzzy Hopfield neural networks and an efficient learning algorithm. Fuzzy Sets and Systems, 112, 41–49.
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.
Liu, P., & Li, H. (2005). Hierarchical TS fuzzy system and its universal approximation. Information Sciences, 169, 279–303.
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.
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.
Mitra, S., & Hayashi, Y. (2000). Neuro-fuzzy rule generation: Survey in soft computing framework. IEEE Transactions on Neural Networks, 11(3), 748–768.
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.
Nauck, D., Klawonn, F., & Kruse, R. (1997). Foundations of neuro-fuzzy systems. New York: Wiley.
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.
Nikov, A., & Stoeva, S. (2001). Quick fuzzy backpropagation algorithm. Neural Networks, 14, 231–244.
Nunez, H., Angulo, C., & Catala, A. (2002). Rule extraction from support vector machines. In Proceedings of European Symposium on Artificial Neural Networks (pp. 107–112).
Nunez, H., Angulo, C., & Catala, A. (2006). Rule-based learning systems for support vector machines. Neural Processing Letters, 24, 1–18.
Omlin, C. W., & Giles, C. L. (1996). Extraction of rules from discrete-time recurrent neural networks. Neural Networks, 9, 41–52.
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.
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.
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.
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.
Simpson, P. K. (1992). Fuzzy min–max neural networks—Part I: Classification. IEEE Transactions on Neural Networks, 3, 776–786.
Simpson, P. K. (1993). Fuzzy min–max neural networks—Part II: Clustering. IEEE Transactions on Fuzzy Systems, 1(1), 32–45.
Sisman-Yilmaz, N. A., Alpaslan, F. N., & Jain, L. (2004). ANFIS-unfolded-in-time for multivariate time series forecasting. Neurocomputing, 61, 139–168.
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.
Stoeva, S., & Nikov, A. (2000). A fuzzy backpropagation algorithm. Fuzzy Sets and Systems, 112, 27–39.
Sun, C. T. (1994). Rule-base structure identification in an adaptive-network-based inference system. IEEE Transactions on Fuzzy Systems, 2(1), 64–79.
Sussner, P., & Valle, M. E. (2006). Implicative fuzzy associative memories. IEEE Transactions on Fuzzy Systems, 14(6), 793–807.
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.
Tsujinishi, D., & Abe, S. (2003). Fuzzy least squares support vector machines for multiclass problems. Neural Networks, 16, 785–792.
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 (Vol. 3, pp. 256–263). London: Chapman & Hall.
Vuorimaa, P. (1994). Fuzzy self-organizing map. Fuzzy Sets and Systems, 66(2), 223–231.
Wang, L. X. (1999). Analysis and design of hierarchical fuzzy systems. IEEE Transactions on Fuzzy Systems, 7(5), 617–624.
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.
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.
Wang, L. X., & Wei, C. (2000). Approximation accuracy of some neuro-fuzzy approaches. IEEE Transactions on Fuzzy Systems, 8(4), 470–478.
Wu, S., & Er, M. J. (2000). Dynamic fuzzy neural networks—A novel approach to function approximation. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 30(2), 358–364.
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.
Zhang, D., Bai, X. L., & Cai, K. Y. (2004). Extended neuro-fuzzy models of multilayer perceptrons. Fuzzy Sets and Systems, 142, 221–242.
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.
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Du, KL., Swamy, M.N.S. (2019). Neurofuzzy Systems. In: Neural Networks and Statistical Learning. Springer, London. https://doi.org/10.1007/978-1-4471-7452-3_27
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DOI: https://doi.org/10.1007/978-1-4471-7452-3_27
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