A Fast Learning Algorithm For Uninorm-based Fuzzy Neural Networks

Abstract

This paper suggests a fast learning algorithm for weighted uninorm-based neural networks. Fuzzy neural networks are models capable to approximate functions with high accuracy and to generate transparent models through extraction of linguistic information from the resulting topology. A fuzzy neural network model based on weighted uninorms has been developed recently. It was shown that this model approximates any continuous real function on a compact subset. In this paper we introduce a fast learning algorithm for this class of fuzzy neural networks based on ideas from extreme learning machine. The algorithm is detailed and computational experiments reported to illustrate the accuracy and time efficiency of the learning approach. The results show that neural fuzzy model is accurate and learning speed is as good as or faster than alternative neural network models. © 2012 IEEE.Minist. Commun. Inf. Technol. Republic AzerbaijanPedrycz, W., Fuzzy Neural Networks and Neurocomputations (1993) Fuzzy Sets and Systems, 56 (1), pp. 1-28. , MAY 25Caminhas, W., Tavares, H., Gomide, F., Pedrycz, W., Fuzzy sets based neural networks: Structure, learning and applications (1999) Journal of Advanced Computational Intelligence, 3 (3), pp. 151-157Gomide, F., Pedrycz, W., (2007) Fuzzy Systems Engineering: Toward Human-Centric Computing, , NJ, USA: Wiley InterscienceBallini, R., Gomide, F., Learning in recurrent, hybrid neurofuzzy networks (2002) IEEE International Conference on Fuzzy Systems, pp. 785-791Hell, M., Costa, P., Gomide, F., Participatory learning in power transformers thermal modeling (2008) IEEE Transactions on Power Delivery, 23 (4), pp. 2058-2067. , OctGobi, A.E., Pedrycz, D., Logic minimization as an efficient means of fuzzy structure discovery (2008) IEEE Transactions on Fuzzy Systems, 16 (3), pp. 553-566. , JUNPedrycz, W., Logic-based fuzzy neurocomputing with unineurons (2006) IEEE Transactions on Fuzzy Systems, 14 (6), pp. 860-873. , DECPedrycz, W., Hirota, K., Uninorm-based logic neurons as adaptive and interpretable processing constructs (2007) Soft Computing, 11 (1), pp. 41-52. , JANHell, M., Gomide, F., Ballini, R., Costa, P., Uninetworks in time series forecasting (2009) NAFIPS 2009. Annual Meeting of the North American Fuzzy Information Processing Society, 2009, pp. 1-6. , juneLemos, A., Caminhas, W., Gomide, F., New uninorm-based neuron model and fuzzy neural networks (2010) 2010 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1-6Lemos, A., Kreinovich, V., Caminhas, W., Gomide, F., Universal approximation with uninorm-based fuzzy neural networks (2011) 2011 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1-6. , marchYager, R., Rybalov, A., Uninorm aggregation operators (1996) Fuzzy Sets and Systems, 80 (1), pp. 111-120. , MAY 27Calvo, T., Baets, B.D., Fodor, J., The functional equations of frank and alsina for uninorms and nullnorms (2001) Fuzzy Sets and Systems, 120 (3), pp. 385-394Herrera, F., Lozano, M., Verdegay, J.L., Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis (1998) Artif. Intell. Rev., 12 (4), pp. 265-319Huang, G.-B., Zhu, Q.-Y., Siew, C.-K., Extreme learning machine: A new learning scheme of feedforward neural networks (2004) 2004 IEEE International Joint Conference on Neural Networks (IJCNN), 2, pp. 985-990. , july vol.2Huang, G.-B., Chen, L., Siew, C.-K., Universal approximation using incremental constructive feedforward networks with random hidden nodes (2006) Neural Networks, IEEE Transactions on, 17 (4), pp. 879-892. , julyYager, R., Uninorms in fuzzy systems modeling (2001) Fuzzy Sets and Systems, 122 (1), pp. 167-175. , AUG 16Huang, G.-B., Siew, C.-K., Extreme learning machine with randomly assigned rbf kernels (2005) International Journal of Information Technology, 11 (1), pp. 16-24Montesino-Pouzols, F., Lendasse, A., Evolving fuzzy optimally pruned extreme learning machine for regression problems (2010) Evolving Systems, 1 (1), pp. 43-58. , AugustBartlett, P., The sample complexity of pattern classification with neural networks: The size of the weights is more important than the size of the network (1998) IEEE Transactions on Information Theory, 44 (2), pp. 525-536. , marSerre, D., (2002) Matrices: Theory and Applications, , New York, US: Springer- VerlagBox, G.E.P., Jenkins, G., (1990) Time Series Analysis, Forecasting and Control, , Holden-Day, IncorporatedRiedmiller, M., Braun, H., A direct adaptive method for faster backpropagation learning: The rprop algorithm (1993) IEEE International Conference on Neural Networks, 1993, 1, pp. 586-591Jang, J., ANFIS - Adaptive-Network-Based Fuzzy Inference System (1993) IEEE Transactions on Systems Man and Cybernetics, 23 (3