時間序列預測是目前非常重要的領域，在金融市場時間序列中，股票預測是較多人所關注的議題，不論是企業或個人投資客都期望能夠透過預測股價，來獲得經濟收益。本研究使用了非線性的模型預測方法來進行股票預測，使用的模型稱為球型複數類神經模糊推理系統(Sphere complex based neuro-fuzzy inference system, SCNFIS)，SCNFIS為一種複數的類神經模糊系統，可以分為前鑑部和後鑑部兩個部分，其透過球型複數模糊集(Sphere Complex Fuzzy Sets, SCFSs)來實現多目標的預測。相較於過往的研究僅預測單一目標，此方法更符合投資人分散風險、同時觀察多個目標以製定投資策略的需求。為了選出對於多個目標皆有貢獻的特徵，本研究使用了多目標特徵選取方法以選出最佳特徵來訓練模型。在SCNFIS中使用了複數減法聚類法(Subtractive clustering for complex-valued data, SCC)來建立模型的前鑑部，其將原本的減法聚類法的實數範圍擴展至複數範圍。為了解決非線性模型會出現的過度擬合和參數最佳化問題，本研究提出了一種混合式的機器學習方法稱為GDWOA-ACO_R-RLSE來最佳化SCNFIS的參數，其透過分治法(The Divide-and-conquer method)的概念，使用GDWOA-ACO_R用於最佳化前鑑部的參數，RLSE用於最佳化後鑑部的參數。最後，進行三個實驗來評估所提出的研究方法的可行性。實驗結果顯示和過去文獻相比具有更好的預測性能，驗證了該方法的有效性。;Time series forecasting is currently a very important field. In the financial market, stock prediction is a topic of great interest. Both businesses and individual investors hope to achieve economic gains through stock price forecasting. This study uses a nonlinear modeling approach to stock prediction, employing a model known as the Sphere Complex based Neuro-Fuzzy Inference System (SCNFIS). SCNFIS is a type of complex-valued neuro-fuzzy system, consisting of a front-end and a back-end. It uses Sphere Complex Fuzzy Sets (SCFSs) to achieve multi-objective forecasting. Compared to previous studies that only predict a single target, this method better aligns with the needs of investors to diversify risks and simultaneously observe multiple targets to formulate investment strategies. To select features that contribute to multiple targets, this study employs a multi-objective feature selection method to choose the best features for training the model. In SCNFIS, a complex-valued subtractive clustering method (SCC) is used to establish the antecedent parts of the model, extending the range of the original subtractive clustering method from real numbers to complex numbers. To address issues of overfitting and parameter optimization in non-linear models, this study proposes a hybrid machine learning method called GDWOA-ACO_R-RLSE to optimize the parameters of SCNFIS. This method uses the concept of the Divide-and-Conquer method, employing GDWOA-ACO_R to optimize the parameters of the front-end and RLSE to optimize the parameters of the back-end. Finally, three experiments are conducted to evaluate the feasibility of the proposed research method. The experimental results show better forecasting performance compared to previous literature, confirming the effectiveness of the method.
