本論文研究中之預測模型為複數模糊類神經模型，藉由複數模糊集(Complex fuzzy set)取代傳統模糊類神經模型(Fuzzy neural network)中使用的傳統模糊集，並採用混合式機器學習進行模型參數學習，包含提出以粒子群最佳化(Particle Swarm Optimization, PSO)與隨機最佳化(Random Optimization, RO)並行運作之演算法，以及遞迴最小平方估計法(Recursive least squares estimator, RLSE)。另外，資料進入模型學習前，先經由基於夏農資訊熵(Shannon Entropy)的特徵選取方法，選出對目標有影響力之特徵作為模型輸入。特徵選取方法是藉由計算特徵對於目標提供的資訊量多寡，來進行特徵的挑選。複數模糊集合比傳統的模糊集合具有更多的空間以附載更多的資訊，運用於模糊類神經網路時，使在神經網路內部傳遞訊息時，能夠包含更大量的資訊，提升模型預測準確度，且藉用複數的性質，模型能夠進行多目標的處理。在機器學習階段，藉由粒子群最佳化與隨機最佳化的並行運作，並透過競爭與學習的策略，增加找到更佳解的機率，再加上與遞迴最小平方估計法作結合，來提升模型運算效率。在模型預測方面，本論文以股票與匯率作為實驗對象，並從實驗結果顯示本論文提出之混合式機器學習、特徵選取與模型都有良好的表現。

In the study, the predictive model is a complex fuzzy neural model. The complex fuzzy sets are used to replace the traditional fuzzy set used in the traditional fuzzy neural network. Based on parallel operation with the particle swarm optimization (PSO) algorithm and the random optimization (RO) algorithm, an improved algorithm is proposed, and combined with the recursive least squares estimation (RLSE) into a hybrid machine learning algorithm, called the RoPso-RLSE learning method. In addition, a feature selection method based on Shannon entropy is presented to select useful features which will be used as model inputs in modeling. In this study, the feature selection, complex neural fuzzy system and hybrid machine learning algorithm are used for time series prediction of stock price and exchange rate. The feature selection selects features by calculating the information provided by the features for the targets. Complex fuzzy sets (CFSs) have better description for set-element relationship than tradition fuzzy sets in membership. They can be used in neural fuzzy networks to transmit more information and increasing the prediction performance of model. Moreover, due to the property of CFSs, the model can perform multi-target forecasting simultaneously. In the machine learning stage, the hybrid algorithm RoPso, compared to use single PSO or RO only, can increase the probability of finding the optimal solution, with fast learning convergence. In addition, combining the RLSE with RoPso can reduce the loading of machine learning by the RoPso alone. Several real-world data sets of stock prices and exchange rates have been used to test the proposed approach in the experiments for multi-objective prediction. Through the experimental results, the proposed approach has shown good performance.

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1 研究背景與目的 1
1.2 研究方法 1
1.3 論文架構 2
第二章 文獻探討 3
2.1 特徵選取 3
2.2 模糊集合 4
2.3 複數模糊集合 7
2.4 模糊類神經網路 8
2.5 機器學習演算法 10
2.5.1 隨機最佳化演算法 11
2.5.2 粒子群最佳化演算法 12
第三章 系統設計與架構 14
3.1 特徵選取 14
3.2 複數模糊類神經模型 17
3.3 混合式機器學習演算法 20
3.3.1 並行式最佳化RoPso 20
3.3.2 遞迴最小平方估計法 24
3.4 研究整體流程 25
第四章 實驗實作與結果 28
4.1 實驗1: 雙目標股票指數預測 28
4.2 實驗2: 三目標股票指數預測 35
4.3 實驗3: 四個目標匯率預測 41
第五章 實驗結果討論 51
第六章 結論 54
6.1 結論 54
6.2 未來研究方向 55
參考文獻 57
附錄 60

[1] O. Reyes, C. Morell and S. Ventura, “Scalable extensions of the ReliefF algorithm for weighting and selecting features on the multi-label learning context,” Neurocomputing., vol. 161, pp. 168-182, August 2015.
[2] I. Guyon et al., “Gene selection for cancer classification using support vector machines,” Machine Learning, vol. 46, issue 1–3, pp. 389–422, January 2002.
[3] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, issue 3, pp. 338-353, June 1965.
[4] D. Ramot, “Complex fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol. 10, issue 2, pp. 171-186, April 2002.
[5] J.-S.R. Jang, “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Transactions on Systems, vol. 23, issue 3, pp. 665-685, May 1993.
[6] George S. Atsalakis and Kimon P. Valavanis, “Forecasting stock market short-term trends using a neuro-fuzzy based methodology,” Expert Systems with Applications, vol. 36, issue 7, pp.10696-10707, September 2009.
[7] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proceedings of ICNN'95 - International Conference on Neural Networks, Perth, WA, Australia, Australia, 1995.
[8] Matyas, J, “Random optimization, “Automation and Remote Control, vol. 26, pp. 244-251, 1965.
[9] F. J. Solis & J. B. Wets, “Minimization by random search techniques. Mathematics of Operations Research”, Mathematics of Operations Research, vol. 6, no. 1, pp. 19-30, February 1981.
[10] N. Baba, T. Shoman, & Y. Sawaragi, “A modified convergence theorem for a random optimization method,” Information Sciences, vol. 13, issue 2, pp. 159-166, 1977.
[11] N. Baba, “Convergence of a random optimization method for constrained optimization problems,” Journal of Optimization Theory and Applications, vol. 33, issue 4, pp. 451-461, April 1981.
[12] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, issue 1, pp. 116–132, January - February 1985.
[13] E.H. Mamdani, “Applications of fuzzy algorithm for control a simple dynamic plant,” Proceedings of the Institution of Electrical Engineers, vol. 121, issue 12, pp. 1585–1588, December 1974.
[14] E.H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” International Journal of Man–Machine Studies, vol. 7, issue 1, pp. 1–13, January 1975.
[15] N. Laptev, “Time-series extreme event forecasting with neural networks at Uber,” International Conference on Machine Learning, Australia, 2017.
[16] P. Singh, “Rainfall and financial forecasting using fuzzy time series and neural networks based model,” International Journal of Machine Learning and Cybernetics, vol. 9, issue 3, pp. 491-506, March 2018.
[17] D. Pradeepkumar and V. Ravi, “Forecasting financial time series volatility using Particle Swarm Optimization trained Quantile Regression Neural Network,” Applied Soft Computing, vol. 58, pp. 35-52, September 2017.
[18] A. Yadav and K. Sahu, “Wind forecasting using artificial neural networks: a survey and taxonomy,” International Journal of Research In Science & Engineering, vol. 3, issue 2, pp. 148-155, March-April 2017.
[19] G. Asencio-Cortés, “A medium–large earthquake magnitude prediction in Tokyo with artificial neural networks,” Neural Computing and Applications, vol. 28, issue 5, pp. 1043–1055, May 2017.
[20] K. Lang, “Short-term load forecasting based on multivariate time series prediction and weighted neural network with random weights and kernels,” Cluster Computing, pp. 1-9, 2018.
[21] C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, issue 3, pp. 379-423, July 1948.
[22] M. R. Hassan and B. Nath, “Stock market forecasting using hidden Markov model: a new approach,” 5th International Conference on Intelligent System Design and Application, Warsaw, Poland, 2005, pp. 192–196.
[23] M. R. Hassan, “A combination of hidden Markov model and fuzzy model for stock market,” Neurocomputing, vol. 72, issue 16-18, pp. 3439-3446, October 2009.
[24] L. Yua, K. K. Lai, and S. Wang, “Multistage RBF neural network ensemble learning for exchange rates forecasting,” Neurocomputing, vol. 71, issues 16–18, Pages 3295–3302, October 2008.
[25] C. Li and T. Chiang, “Complex neuro fuzzy ARIMA forecasting-a New approach using complex fuzzy sets,” IEEE Transactions on Fuzzy Systems, vol. 21, issue 3, pp. 567-584, June 2013.
[26] Κ. J. Astrom, Β. Wittenmark, Adaptive Control, ΜA, Reading: Addison-Wesley, 1989.
[27] O. D. Crisalle, “Adaptive Control of Photolithography,” American Institute of Chemical Engineers Journal, vol. 38, issue 1, pp. 1-14. , January 1992.
[28] R.C. Eberhart and Shi, Y. “Tracking and Optimizing Dynamic Systems with Particle Swarms,” Proceedings of the Congress on Evolutionary Computation, Seoul, South Korea, 2001, pp. 94–100.
[29] A. Chatterjee and P. Siarry, “Nonlinear Inertia Weight Variation for Dynamic Adaptation in Particle Swarm Optimization,” Computers and Operations Research, vol. 33, Issue 3, pp. 859-871, March 2006.
[30] Shu-Kai S. Fan, and E. Zahara, “A Hybrid Simplex Search and Particle Swarm Optimization for Unconstrained Optimization” European Journal of Operational Research, vol. 181, issue 2, pp. 527-548, September 2007.
[31] M. Clerc and J. Kennedy, “The Particle Swarm:Explosion, Stabiliry, and Convergence in a Multimodal Complex Space.” Proceeddings of the Congress of Evolutionary Computation, Washington, DC, IEEE, Piscataway, NJ, USA, vol. 6, 2000, pp.58-73.
[32] A. Colorni, M. Dorigo, and V. Maniezzo, “Distributed Optimization by Ant Colonies,” The European Conference on Artificial Life, Paris, France, 1991, pp. 134-142.
[33] J. H. Holland, Adaptation in Natural and Artificial Systems, MA, Cambridge: MIT Press, 1992.
[34] A. Kazem, “Support vector regression with chaos-based firefly algorithm for stock market price forecasting,” Applied Soft Computing, vol. 13, no. 2, pp. 947-958, February 2013.
[35] J.-S. Jang, C.-T. Sun, and E. Mizutani, “Neuro-Fuzzy and Soft Computing: a computational approach to learning and machine intelligence,” ISBN 0-13-261066-3, Prentice Hall, Upper Saddle River, NJ, USA, 1997.
[36] J.J. Choi, S. Oh, R.J. Marks, “ “Training layered perceptrons using low accuracy computation,” Proceedings IEEE International Joint Conference on Neural Networks, vol. 1, pp. 554-559, 1991.
[37] 國立中央大學資訊管理所李俊賢教授, 研究生訓練課程內容2016-2018 (包含多目標特徵選取與RoPso設計概念), 紀錄筆記。 (未發表)