在本論文中，我們根據模糊邏輯關係、模糊趨勢邏輯關係群、K-Means分群演算法、相似度測量及粒子群最佳化技術提出兩個模糊預測之新方法以處理預測問題。在本論文所提之第一個方法中，我們根據模糊邏輯關係、粒子群最佳化技術、K-Means分群演算法及模糊集合下標之相似度測量提出一個模糊預測新方法以預測台灣股價加權指數，其中我們利用粒子群最佳化技術以得到論述宇集區間最佳化之分割、利用K-Means分群演算法以將模糊邏輯關係之目前狀態中的模糊集合之下標作分群及得到每一個群之群中心，並將已建立之模糊邏輯關係分為若干個模糊邏輯關係群、及利用模糊集合下標之相似度測量值作為權重以預測台灣股價加權指數。在本論文所提之第二個方法中，我們提出根據兩因子兩階模糊趨勢邏輯關係群、粒子群最佳化技術及模糊集合之下標之間的相似度測量提出一個新方法以預測台灣股價加權指數及台幣與美金之間的匯率，其中我們利用粒子群最佳化技術以得到論述宇集區間最佳化之分割、利用模糊集合下標之相似度測量值以篩選模糊趨勢邏輯關係群中之模糊邏輯關係、及利用趨勢機率以預測台灣股價加權指數及台幣與美金之間的匯率。實驗結果顯示我們所提之方法比目前已存在之方法具有更高之預測準確率。

In this thesis, we propose two new fuzzy forecasting methods to deal with forecasting problems based on fuzzy logical relationships, fuzzy-trend logical relationship groups, K-means clustering algorithm, similarity measures and particle swarm optimization (PSO) techniques. In the first method of this thesis, we propose a new method for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series, fuzzy logical relationships, particle swarm optimization (PSO) techniques, the K-means clustering algorithm, and similarity measures between the subscripts of the fuzzy sets, where we use PSO techniques to get the optimal partition of the intervals in the universe of discourse, use the K-means clustering algorithm to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups, and use similarity measures between the subscripts of the fuzzy sets for forecasting the TAIEX. In the second method of this thesis, we propose a new method for forecasting the TAIEX and the NTD/USD exchange rates based on two-factors second-order fuzzy-trend logical relationship groups, PSO techniques and similarity measures between the subscripts of fuzzy sets, where we use PSO techniques to get the optimal partition of the intervals in the universe of discourse, use similarity measures between the subscripts of the fuzzy sets to choose fuzzy logical relationships from the fuzzy-trend logical relationship group, and use the probabilities of trends for forecasting the TAIEX and the NTD/USD exchange rates. The experimental results show that the proposed methods get higher forecasting accuracy rates than the existing methods.

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