Hybrid Neurofuzzy Computing With Nullneurons

In this paper we address a new type of elementary neurofuzzy unit called nullneuron. A nullneuron is a generalization of and/or neurons based on the concept of nullnorm, a category of fuzzy sets operators that generalizes triangular norms and conorms. The nullneuron model is parametrized by an element u, called the absorbing element. If the absorbing element u = 0, then the nullneuron becomes a and neuron and if u = 1, then the nullneuron becomes a dual or neuron. Also, we introduce a new learning scheme for hybrid neurofuzzy networks based on nullneurons using reinforcement learning. This learning scheme adjusts the weights associated with the individual inputs of the nullneurons, and learns the role of the nullneuron in the network (and or or) by individually adjusting the parameter u of each nullneuron. Nullneuron-based neural networks and the associated learning scheme is more general than similar neurofuzzy networks because they allow different triangular norms in the same network structure. Experimental results show that nullneuron-based networks provide accurate results with low computational effort. © 2008 IEEE.36533659Lin, C.C., Lee, C.S.J., Neural network based fuzzy logic control and decision system (1991) IEEE Trans. on Systems Man and Cybernetics, 40 (12), pp. 1320-1336Jang, R., ANFIS: Adaptive network based fuzzy inference system (1993) IEEE Trans. on Systems Man and Cybernetics, 23 (3), pp. 665-685Lin, C.T., Lee, C.S., (1996) Neural Fuzzy Systems, , Prentice Hall, NJ, USAKosko, B., (1991) Neural Networks and fuzzy Systems: A Dynamical System Approach to Machine Intelligence, , Prentice HallFigueiredo, M., Ballini, R., Soares, S., Andrade, M., Gomide, F., Learning Algorithms for a class of Neurofuzzy Network and Application (2004) IEEE Trans. on System, Man and Cybernetics - Part C, 34 (3), pp. 293-301Pedrycz, W., Fuzzy neural networks and neurocomputations (1993) Fuzzy Sets and Systems, 56 (1), pp. 1-28Yager, R., Rybalov, A., Uninorm aggregation operators (1996) Fuzzy Sets and Systems, 80 (1), pp. 111-120Calvo, T., De Baets, B., Fodor, J., The functional equations of Frank ans Alsina for uninorms and nullnorms (2001) Fuzzy Sets Syst, 120, pp. 385-394Rutkowski, L., Cpalka, K., Flexible neuro-fuzzy systems (2003) IEEE Trans. on Neural Networks, 14 (3), pp. 554-574Rutkowski, L., Cpalka, K., Design and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems (2005) IEEE Trans. on Neural Networks, 13 (1), pp. 140-151Pedrycz, W., Logic-based neurocomputing with unineurons (2006) IEEE Trans. on Fuzzy Syst, 14 (6), pp. 860-873Hell, M., Costa Jr., P., Gomide, F., Nullneurons-Based Hybrid Neurofuzzy Network (2007) Proceedings of Annual Meeting of the North American Fuzzy Information Processing Society, 2007. NAFIPS '07, pp. 331-336Gomide, F., Pedrycz, W., Fuzzy Systems Engineering: Toward Human-Centric Computing (2007) Wiley Interscience, , Hoboken, NJ, USAHetch-Nielsen, R., (1989) Neurocomputing, , San Diego, CA: Addison WesleyBarto, A.G., Jordan, M.I., Gradient following without backpropagation in layered networks (1987) Proc. of the IEEE First International Conference on Neural Networks, 2, pp. 629-636. , San DiegoCaminhas, W., Tavares, H., Gomide, F., Pedrycz, W., Fuzzy set based neural networks: Structure, Learning and Application (1999) Journal of Advanced Computational Intelligence, 3 (3), pp. 151-157Box, G.E.P., Jenkins, G.M., (1976) Time Series Analysis- Forecasting and Control, , 2.ed, Holden Day, CA, USATong, R.M., The Evaluation of Fuzzy Models Derived from Experimental Data (1980) Fuzzy Sets and Systems, 4, pp. 1-12Farag, W.A., Quintana, V.H., Lambert-Torres, G., A genetic-based neuro-fuzzy approach for modeling and control of dynamical systems (1998) IEEE Trans. Neural Networks, 9 (5), pp. 756-767. , SepXiao-Zhi, G., Ovaska, S.J., Linguistic information feedforward-based dynamical fuzzy systems (2006) IEEE Transactions on Systems, Man and Cybernetics, Part C, 36 (4), pp. 453-463. , JulyPedrycz, W., A Identification Algorithm in Fuzzy Relational Systems (1984) Fuzzy Sets and Systems, 13, pp. 153-167Xu, W., Lu, Y.Z., Fuzzy Model Identification and Self-learning for Dynamic Systems (1987) IEEE Trans. on System, Man and Cybernetics, SMC-17, pp. 683-689. , JulyDelgado, M., Gmez-Skarmeta, A.F., Martin, F., Fuzzy Clustering based Rapid Prototyping for Fuzzy Rule-based Modeling (1997) IEEE Trans. on Fuzzy Systems, 5, pp. 223-233. , MayYoshinari, Y., Pedrycz, W., Hirota, K., Construction of Fuzzy Models Through Clustering Techniques (1993) Fuzzy Sets and Systems, 54, pp. 157-16