本論文將傳統模糊類神經網路等效轉換為全連接之三層模糊類神經網路，並利用全連接模糊類神經網路探討網路的容量，其中容量代表在完善的訓練法下可零誤差映射到期望輸出的最大樣本數量。本論文亦提出了一種新的訓練方法 — 雙階訓練法，此方法將模糊類神經網路分成兩部分進行訓練，其可在較少的疊代次數下使得網路模型具有更好的分類能力，並且有效解地決網路在訓練過程有損失函數值上升的問題；除此之外，模糊類神經網路之性能相較傳統的訓練方法亦有效的提升。本論文亦使用鳶尾花和每日漁獲量數據集作為模擬的訓練資料，從實驗模擬表明，雙階訓練法具有更佳的訓練效能外，還能以更少的疊代次數、更短的運算時間來達到較高之準確率。

In this thesis, the traditional fuzzy neural network is equivalently converted into a fully connected three-layer fuzzy neural network, which is utilized to discuss the capacity of the neural network, i.e., the maximum number of samples that can be exactly mapped to the desired output with zero error under a well training method. This thesis also proposes a new training method—two-stage training approach. This strategy divides the overall training process into two parts so that the trained network has better classification capabilities with fewer (relatively less) iterations in training. In addition, the two-stage training approach effectively solves the problem that the loss function of the network probably increases during training processes. Furthermore, the performance of the model is also effectively improved compared to the traditional training approach. Iris and daily fish catch datasets are used as training data for the simulations, which show that the proposed two-stage training approach not only has better training performance but also achieves higher accuracy with fewer iterations and shorter computing time.

[1] W. S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,” The bulletin of mathematical biophysics, vol. 5, no. 4, pp. 115–133, 1943.
[2] D. O. Hebb, The Organization of Behavior. John Wiley & Sons, 1949.
[3] F. Rosenblatt, “The perceptron: a probabilistic model for information storage and organization in the brain,” Psychological review, vol. 65, no. 6, pp. 386–408, 1958.
[4] B. Widrow and M. E. Hoff, “Adaptive switching circuits,” IRE WESCOM Conv. REC., vol. 4, pp. 96–104, 1960.
[5] J. L. McClelland and D. E. Rumelhart, Parallel distributed processing. MIT press Cambridge, MA, 1986.
[6] S. C. Lee and E. T. Lee, “Fuzzy neural networks,” Mathematical Biosciences, vol. 23, pp. 151–177, 1975.
[7] A. D. Kulkarni and C. D. Cavanaugh, “Fuzzy neural network models for classification,” Applied Intelligence, vol. 12, no. 3, pp. 207–215, 2000.
[8] J. L. Chen and J. Y. Chang, “Fuzzy perceptron neural networks for classifiers with numerical data and linguistic rules as inputs,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 6, pp. 730–745, 2000.
[9] A. Kulkarni, “Fuzzy neural network for pattern classification,” Procedia Computer Science, vol. 167, pp. 2606–2616, 2020.
[10] H. A. Abdullah, “Neuro-fuzzy inference system based face recognition using feature extraction,” Telkomnika, vol. 18, no. 1, pp. 427–435, 2020.
[11] C. H. Wang, W. Y. Wang, T. T. Lee, and P. S. Tseng, “Fuzzy b-spline membership function (BMF) and its applications in fuzzy-neural control,” IEEE transactions on systems, man, and cybernetics, vol. 25, no. 5, pp. 841–851, 1995.
[12] C. H. Wang and J. S. Wen, “On the equivalence of a table lookup (TL) technique and fuzzy neural network (FNN) with block pulse membership functions (BPMFs) and its application to water injection control of an automobile,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 38, no. 4, pp. 574–580, 2008.
[13] S. Wu and M. J. Er, “Dynamic fuzzy neural networks-a novel approach to function approximation,” IEEE transactions on systems, man, and cybernetics, vol. 30, no. 2, pp. 358–364, 2000.
[14] J. Tang, F. Liu, Y. Zou, W. Zhang, and Y. Wang, “An improved fuzzy neural network for traffic speed prediction considering periodic characteristic,” IEEE Transactions on Intelligent Transportation Systems, vol. 18, no. 9, pp. 2340–2350, 2017.
[15] C.-H. Wang, H.-L. Liu, and C.-T. Lin, “Dynamic optimal learning rates of a certain class of fuzzy neural networks and its applications with genetic algorithm,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 31, no. 3, pp. 467–475, 2001.
[16] S. C. Huang and Y. F. Huang, “Bounds on the number of hidden neurons in multilayer perceptrons,” IEEE transactions on neural networks, vol. 2, no. 1, pp. 47–55, 1991.
[17] M. A. Sartori and P. J. Antsaklis, “A simple method to derive bounds on the size and to train multilayer neural networks,” IEEE transactions on neural networks, vol. 2, no. 4, pp. 467–471, 1991.
[18] J. Wang, C. H. Wang, and C. L. P. Chen, “The bounded capacity of fuzzy neural networks (FNNs) via a new fully connected neural fuzzy inference system (F CONFIS) with its applications,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 6, pp. 1373–1386, 2013.
[19] J. Wang, C. H. Wang, and C. L. Chen, “Finding the capacity of fuzzy neural networks (FNNs) via its equivalent fully connected neural networks (FFNNs),” in 2011 IEEE International Conference on Fuzzy Systems, 2011, pp. 2193–2198.
[20] S. Horikawa, T. Furuhashi, and Y. Uchikawa, “On fuzzy modeling using fuzzy
neural networks with the back-propagation algorithm,” IEEE transactions on Neural Networks, vol. 3, no. 5, pp. 801–806, 1992.
[21] P. Liu and H. Li, “Efficient learning algorithms for three-layer regular feedforward fuzzy neural networks,” IEEE Transactions on Neural Networks, vol. 15, no. 3, pp. 545–558, 2004.
[22] X. H. Yu, G. A. Chen, and S. X. Cheng, “Dynamic learning rate optimization of the backpropagation algorithm,” IEEE Transactions on Neural Networks, vol. 6, no. 3, pp. 669–677, 1995.
[23] J. X. Peng, K. Li, and G. W. Irwin, “A new jacobian matrix for optimal learning of single-layer neural networks,” IEEE transactions on neural networks, vol. 19, no. 1, pp. 119–129, 2008.
[24] C. H. Wang, K. C. Hor, and B. Wang, “Identifying an unknown flying target in missile defense systems using intelligent fuzzy neural networks,” in 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery, 2018, pp. 1127–1132.
[25] A. Famili,W. M. Shen, R.Weber, and E. Simoudis, “Data preprocessing and intelligent data analysis,” Intelligent data analysis, vol. 1, no. 1, pp. 2–23, 1997.
[26] S. B. Kotsiantis, D. Kanellopoulos, and P. E. Pintelas, “Data preprocessing for supervised leaning,” International Journal of Computer Science, vol. 1, no. 2, pp. 111–117, 2006.
[27] D. G. Luenberger, Y. Ye, and others., Linear and nonlinear programming. Springer, 1984.
[28] W. Wu, L. Li, J. Yang, and Y. Liu, “A modified gradient-based neurofuzzy learning algorithm and its convergence,” Information Sciences, vol. 180, no. 9, pp. 1630–1642, May 2010.
[29] E. H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” International journal of man-machine studies, vol. 7, no. 1, pp. 1–13, 1975.
[30] E. H. Mamdani, “Application of fuzzy algorithms for control of simple dynamic plant,” Proc. Inst. Elect. Eng., vol. 121, no. 12, pp. 1585–1588, 1974.
[31] M. N. H. Siddique and M. O. Tokhi, “Training neural networks: backpropagation vs. genetic algorithms,” in Proc. Int. Joint Conf. Neural Netw, vol. 4, pp. 2673–2678, 2001.
[32] A. K. Palit, G. Doeding, W. Anheier, and D. Popovic, “Backpropagation based training algorithm for takagi-sugeno type mimo neuro-fuzzy network to forecast electrical load time series,” in Proc. IEEE Int. Conf. Fuzzy Syst., vol. 1, pp. 86–91, 2002.
[33] S. Tong and H. X. Li, “Fuzzy adaptive sliding-mode control for MIMO nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 3, pp. 354–360, 2003.
[34] Y. J. Liu, W. Wang, S. C. Tong, and Y. S. Liu, “Robust adaptive fuzzy output feedback control,” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, vol. 40, no. 1, pp. 170–184, 2009.
[35] S. Islam and P. X. Liu, “Robust adaptive fuzzy output feedback control system for robot manipulators,” IEEE Trans. Fuzzy Syst., vol. 16, no. 2, pp. 288–296, 2011.
[36] C. L. P. Chen, J.Wang, C. H.Wang, and L. Chen, “A new learning algorithm for a fully connected neuro-fuzzy inference system,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 10, pp. 1741–1757, 2014.
[37] G. B. Huang and H. A. Babri, “Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions,” IEEE transactions on neural networks, vol. 9, no. 1, pp. 224–229, 1998.
[38] P. L. Narasimha, M. T. Manry, and F. Maldonado, “Upper bound on pattern storage in feedforward networks,” in International Joint Conference on Neural Networks, Orlando, FL, USA, Agu. 2007, pp. 1714–1719.
[39] J. Han, M. Kamber, and J. Pei, Data Mining Concepts and Techniques. Morgan Kaufmann Publishers, 2011.
[40] K. Pearson, “On lines and planes of closest fit to systems of points in space,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 2, no. 11, pp. 559–572, 1901.
[41] J. Han, M. Kamber, and J. Pei, Data Mining Concepts and Techniques. Morgan Kaufmann Publishers, 2012.
[42] I. T. Jolliffe and J. Cadima, “Principal component analysis: a review and recent developments,”Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, vol. 374, no. 2065, 2016.
[43] Y. Dodge, he concise encyclopedia of statistics. Springer Science & Business Media, 2008.
[44] X. J. Zeng and M. G. Singh, “Approximation accuracy analysis of fuzzy systems as function approximators,” IEEE Transactions on fuzzy systems, vol. 4, no. 1, pp. 44–63, 1996.
[45] V. Z. Marmarelis and X. Zhao, “Volterra models and three-layer perceptrons,” IEEE Transactions on Neural Networks, vol. 8, no. 6, pp. 1421–1433, 1997.
[46] M. J. Dreyfus-Leon, “Individual-based modelling of fishermen search behaviour with neural networks and reinforcement learning,” Ecological Modelling, vol. 120, no. 2-3, pp. 287–297, 1999.
[47] P. Yugopuspito, S. Lukas, D. Krisnadi, and S. Albert, “Website design for fishing finder based on vms data in indonesia,” in Proceedings of the 3rd International Conference on Telecommunications and Communication Engineering, 2019, pp. 80–84.