| 摘要: | 由於複數模糊集合 (Complex fuzzy set, CFS) 理論的提出，為模糊系統與其相關的研究帶來一個新的視野。雖然CFS的概念與特性已經被提出探討，但仍未有研究提出一套明確的CFS設計準則與方法，而且運用此概念之相關研究仍然相當少。因此，本研究提出一個新的複數模糊類神經系統 (Complex neuro-fuzzy system, CNFS)，結合複數模糊集合、類神經模糊系統 (neuro-fuzzy system, NFS) 以及自回歸移動平均模型 (Auto-regressive integrated moving average, ARIMA) 並應用於系統建模之研究。本研究提出新的高斯複數模糊集合 (Gaussian CFSs) 來描述模糊法則之前鑑部 (Premise parts)，ARIMA 模型作為法則之後鑑部 (Consequent parts)。複數模糊集合是從模糊集合延伸而來，其歸屬程度可進一步延伸至單位複數圓盤，因而增加歸屬函數描述的能力。藉由複數模糊集合之特性，CNFS-ARIMA模型擁有良好的非線性映射能力。由於 CNFS 模型之輸出為一個複數值，其實部 (Real part) 與虛部 (Imaginary part) 可同時用來處理不同函數之映射，此可稱為雙輸出之特性 (Dual-output property)。為了構建 CNFS-ARIMA 模型，本研究將透過結構學習與參數學習方法來自我建構與調整 CNFS-ARIMA 模型之結構與參數。在結構學習階段，本研究使用模糊 C 平均分裂演算法來自動決定符合樣本資料分布特性的系統架構與法則數目；參數學習階段使用粒子群最佳化演算法 (Particle swarm optimization, PSO) 與遞迴式最小平方估計器 (Recursive least squares estimator, RLSE），稱為 PSO-RLSE 複合式學習演算法，進行系統參數之快速學習。為了測試本研究所提出之方法的效能，本研究使用過去研究常用之標竿系統建模之資料集作為實驗範例，並與文獻所提出之方法進行比較。本研究運用函數逼近與實際的財務經濟時間序列資料，來測試模型雙輸出之實驗。由實驗結果可證實本研究所提出之系統方法可以獲得良好的效能。
Ever since the initiate of the theory of complex fuzzy sets (CFSs), a new vision has dawned upon fuzzy systems and their variants. Although there has been considerable development made in determining the properties of CFSs, the research on complex fuzzy system designs and applications of this concept is found rarely. In this dissertation, we present a novel self-organizing complex neuro-fuzzy intelligent approach using CFSs for the applications of system modeling. The proposed approach integrates a complex neuro-fuzzy system (CNFS) using CFSs and auto-regressive integrated moving average (ARIMA) models to form the proposed computing model, called the CNFS-ARIMA. A class of Gaussian complex fuzzy sets is proposed to describe the premise parts of fuzzy If-Then rules, whose consequent parts are specified by ARIMA models. A CFS is an advanced fuzzy set whose membership degrees are complex-valued within the unit disc of the complex plane, expanding the capability of membership description. With the nature of CFS, the proposed CNFS models have excellent nonlinear mapping capability. Moreover, the output of CNFS-ARIMA is complex-valued, of which the real and imaginary parts can be used for two different functional mappings, respectively. This is the so-called dual-output property. For the formation of CNFS-ARIMA, structure learning and parameter learning are involved to self-organize and self-tune the proposed model. For the structure learning phase, a FCM-based splitting algorithm (FBSA) is used to automatically determine the initial knowledge base of the CNFS-ARIMA. The PSO-RLSE hybrid learning algorithm is proposed for the purpose of fast learning, integrating the particle swarm optimization (PSO) and the recursive least squares estimator (RLSE). A number examples of time series are used to test the proposed approach, whose results are compared with those by other approaches. Moreover, real-world applications of system modeling including function approximation and time series are used for the proposed approach to perform the dual-output forecasting experiments. The experimental results indicate that the proposed approach shows excellent performance. |
