量子波動方法於多目標預測之研究及其應用;A Quantum Wave Approach to Multitarget Prediction and Its Applications

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题名:	量子波動方法於多目標預測之研究及其應用;A Quantum Wave Approach to Multitarget Prediction and Its Applications
作者:	鄭亦傑;Zheng, Yi-Jie
贡献者:	資訊管理學系
关键词:	複數類神經網路;複數模糊集;量子演算法;量子波函數;時間序列;Complex fuzzy neural networks;Complex fuzzy sets;Quantum algorithms;Quantum wave function;Time series
日期:	2025-07-13
上传时间:	2025-10-17 12:33:49 (UTC+8)
出版者:	國立中央大學
摘要:	本研究針對多目標時間序列預測的挑戰，提出三項創新技術，分別為量子波函數導入策略、量子球型複數模糊集（Quantum Sphere Complex Fuzzy Sets, QSCFSs）和量子波動群優化演算法（Quantum Wave Swarm Optimizer, QWSO）。這三項技術的整合目的在全面提升模型的準確性、參數學習之收斂效率與複雜時間序列資料的適應能力。首先，本研究提出量子波函數導入策略，藉由引入不同量子態的氫原子波函數為理論基礎，結合範圍調整公式和逆變換抽樣法，以強化傳統模糊集與演算法之效能表現。其次，本研究提出QSCFSs，將氫原子在不同量子態下之波函數導入至球型複數模糊集(Sphere Complex Fuzzy Sets, SCFSs)，藉以改善SCFSs在角度計算上，缺乏對天頂角和方位角之角度範圍限制的問題，進而強化模型前鑑部在處理多維度複數輸入條件下之精確性與泛化能力。最後，本研究設計QWSO，融合粒子群演算法（Particle Swarm Optimization, PSO）、隨機最佳化演算法（Random Optimization, RO）與黏菌演算法（Slime Mould Algorithm, SMA）之優點，並以量子粒子位置的更新機制為基礎，進而實現更高效的參數訓練與收斂速度。綜合上述技術，本研究構建出量子複數模糊類神經網路（Quantum Complex Fuzzy Neural Network, QCFNN），並採用結合 QWSO 與遞迴最小平方估計法（Recursive Least Squares Estimator, RLSE）之複合式演算法進行模型訓練。經由三項實驗驗證，本研究所提出的方法在不同目標數量與應用情境下，均展現出顯著的預測效能提升，證明量子力學導入於時間序列預測領域之可行性。;This study addresses the challenges of multitarget time series forecasting by proposing three innovative techniques: the quantum wave function embedding strategy, the Quantum Sphere Complex Fuzzy Sets (QSCFSs), and Quantum Wave Swarm Optimizer (QWSO). The integration of these three techniques aims to comprehensively enhance the model’s accuracy, convergence efficiency in parameter learning, and adaptability to complex time series data. First, the quantum wave function embedding strategy is introduced, which incorporates hydrogen atom wave functions under different quantum states as the theoretical foundation. By combining a range-adjustment formula and the inverse transform sampling method, this strategy improves the performance of traditional fuzzy sets and optimization algorithms. Secondly, this study proposes the QSCFSs, which incorporate the wave functions of the hydrogen atom under different quantum states into the traditional Sphere Complex Fuzzy Sets (SCFSs). This approach addresses the lack of constraints on the ranges of zenith and azimuthal angles in SCFSs′ angular calculations, thereby enhancing the precision and generalization capability of the model′s If-part when handling multi-dimensional complex-valued input conditions. Lastly, QWSO is designed by integrating the strengths of Particle Swarm Optimization (PSO), Random Optimization (RO), and Slime Mould Algorithm (SMA). It adopts a quantum particle position updating mechanism to achieve more efficient parameter training and faster convergence. By integrating the aforementioned techniques, this study constructs a Quantum Complex Fuzzy Neural Network (QCFNN) and employs a hybrid training algorithm combining QWSO and the Recursive Least Squares Estimator (RLSE). Experimental validation across three scenarios demonstrates that the proposed approach significantly improves forecasting performance under various target counts and application contexts, thereby confirming the feasibility and effectiveness of incorporating quantum mechanical concepts into time series forecasting.
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