In the paper, a new flexible modification of neofuzzy neuron, neuro-fuzzy network based on these neurons and adaptive learning algorithms for the tuning of their all parameters are proposed. The algorithms are of interest because they ensure the on-line tuning of not only the synaptic weights and membership function parameters but also forms of these functions that provide improving approximation properties and allow avoiding the occurrence of “gaps” in the space of inputs.
 V. Raghavan, A. Hafez “Dynamic Data Mining”, J. of the American Society for Information Science, pp. 220-229, 2000.
 E. Lughofer, Evolving Fuzzy Systems: Methodologies, Advanced Concepts and Applications. Springer, 2011.
 R.H. Abiyev, O. Kaynak “Fuzzy wavelet neural networks for identification and control of dynamic plants - A novel structure and a comparative study”, IEEE Trans. on Industrial Electronics, vol. 55(8), pp. 3133-3140, 2008.
 Ye. Bodyanskiy, I. Pliss, O. Vynokurova, “Adaptive wavelet-neurofuzzy network in the forecasting and emulation tasks”, Int. J. on Information Theory and Applications, vol. 15(1), pp. 47-55, 2008.
 Ye. Bodyanskiy, I. Pliss, O. Vynokurova, “Hybrid wavelet-neuro-fuzzy system using adaptive W-neurons”, Wissenschaftliche Berichte, FH Zittau/Goerlitz, vol. 106(N.2454-2490), pp. 301-308, 2008.
 Ye. Bodyanskiy and I. Pliss and O. Vynokurova Hybrid GMDH-neural network of computational intelligence. Proc. 3rd International Workshop on Inductive Modelling, Poland, Krynica, 2009.
 T. Miki and T. Yamakawa, “Analog implementation of neo-fuzzy neuron and its on board learning”. in Computational Intelligence and Application, N.E. Mastorakis, Ed., WSES Press, 1999, pp. 144-149.
 T. Yamakawa and T. Miki and E. Uchino and H. Kusanagi A neo fuzzy neuron and its applications to system identification and prediction of the system behaviour. Proc. 2-nd Int. Conf. on Fuzzy Logic and Neural Networks - "IIZUKA-92", Iizuka, Japan, 1992.
 E. Uchino and T. Yamakawa, “Soft computing bases signal prediction, restoration, and filtering”, in Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms, Da Ruan, Ed., Boston, Kluwer Academic Publishers, 1997, pp. 331-349.
 Ye. Bodyanskiy and I. Kokshenev and V. Kolodyazhniy An adaptive learning algorithm for a neo fuzzy neuron. Proc. 3-nd Int. Conf. of European Union Society for Fuzzy Logic and Technology (EUSFLAT'03), Zittau, Germany, 2003.
 G.C. Goodwin, P.J. Ramadge, P.E. Caines “A globally convergent adaptive predictor”. Automatica, vol. 17(1), pp. 135-140, 1981.
 Ye.V. Gorshkov, V.V. Kolodyazhniy, I.P. Pliss “Adaptive learning algorithm for a neo-fuzzy neuron and neuro-fuzzy network based on a polynomial membership functions”, Bionica Intellecta: Sci. Mag., vol. 61(1), pp. 78-81, 2004.
 Ye. Bodyanskiy, Ye. Viktorov, “The cascade neo-fuzzy architecture using cubic-spline activation functions”, Int. J. Information Theories and Application, vol. 16(3), pp. 245-259, 2009.
 V. Kolodyazhniy, Ye. Bodyanskiy, Cascaded multiresolution splinebased fuzzy neural network. Eds. P. Angelov, D. Filev, N.Kasabov. Proc. Int. Symp. on Evolving Intelligent Systems, Leicester, UK, 2010.
 Ye. Bodyanskiy, N. Lamonova, I. Pliss, O. Vynokurova, “An adaptive learning algorithm for a wavelet neural network”, Expert Systems, vol. 22(5), pp. 235-240, 2005.
 Ye. Bodyanskiy, O. Vynokurova, “Hybrid adaptive wavelet-neuro-fuzzy system for chaotic time series identification”, Information Science, vol. 220, pp. 170-179, 2013.
 L.X. Wang, J. Mendel, “Generating fuzzy rules by learning from examples” IEEE Trans. Syst., Man, and Cyb., vol. 22, pp. 1414-1427, 1992.
 J.-S. Jang, C.-T. Sun, and E. Mizutani Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice Hall, 1997.