模糊類神經系統（Neuro-fuzzy system, NFS）結合了人工神經網絡（Artificial neural network, ANN）的學習能力和模糊推論系統（Fuzzy inference system, FIS）明確表達知識的能力。然而，傳統模糊類神經系統存在兩個問題影響了系統運作的效率，這兩個問題分別為模型的對稱結構和多輸入單輸出架構。本篇論文提出非對稱式模糊類神經系統（Asymmetric NFS, ANFS），此系統包含兩種機制解決上述存在於傳統模糊類神經系統的問題。首先，非對稱式模糊類神經系統中加入了非對稱層（Asymmetric layer）的結構，使得模型前鑑部層（Premise layer）與後鑑部層（Consequent layer）可以擁有不同的神經元數量。其次，模型使用球型複數模糊集（Sphere complex fuzzy sets, SCFSs）取代位於前鑑部層的傳統模糊集，使模型可以依據不同應用彈性調整輸出數量。此外，為了解決多目標預測模型所衍生的跨目標特徵選擇問題，論文中提出以影響資訊為基礎的跨目標特徵選擇演算法。而因應模型前鑑部層參數為非線性、後鑑部層參數為線性的特性，也提出了一個結合以狀態為基礎的鯨群優化演算法（State-based whale optimization algorithm, SWOA）和遞迴式最小平方估計法（Recursive least-square estimator, RLSE）的混合型學習演算法來優化模型參數。
論文設計三個實驗來驗證所提出方法的效能，包含雙函數近似、雙匯率預測、以及四個股票指數的預測。實驗結果顯示，所提出的方法可以同時對多個目標進行預測，且預測效能優於傳統模糊類神經系統與多數文獻中的方法。

The neuro-fuzzy system (NFS) is designed to exploit the learning abilities of an artificial neural network (ANN) and the explicit knowledge of a fuzzy inference system (FIS). However, the two problems of symmetric structure and the multiple-input single-output architecture in traditional NFSs affect system efficiency. An asymmetric NFS (ANFS) has been proposed in this dissertation to address the problems mentioned above with two mechanisms. Firstly, an asymmetric layer is added to the ANFS model, making the model has different neuron numbers in the premise and consequent layers. Secondly, the introduced sphere complex fuzzy sets (SCFSs) replace the traditional fuzzy sets, making the model output numbers adjustable for different applications. For resolving the cross-target feature selection problem existing in the multitarget prediction model, we proposed a feature selection algorithm based on influence information. Besides, a hybrid learning algorithm combining a state-based whale optimization algorithm with the recursive least-square estimator has been proposed to optimize the model.
Three experiments are designed to evaluate the proposed approach’s performance, including the dual function approximation, two exchange rate, and four stock index predictions. The experimental results indicate that the proposed approach can predict multiple targets simultaneously, having a favorable performance better than conventional NFS and other methods in the literature.

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