Fuzzy time series have been widely used in solving forecasting problem, such as the enrollments forecasting, the temperature forecasting, the stock index forecasting, the exchange rates forecasting, …, etc. Particle swarm optimization is a swarm-based optimization method that can find a near optimal solution for any kind of optimization problems. Therefore, if we can use it appropriately to determine the optimal proportion of the data in the current dates in calculating the data in the next date, we can get a nearly-optimal solution. In this thesis, we present a new method for fuzzy forecasting based on two-factors high-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. First, we fuzzify the historical training data of the main factor and the secondary factor, respectively, to form two-factors high-order fuzzy logical relationships. Then, we group the two-factors high-order fuzzy logical relationships into two-factors high-order fuzzy-trend logical relationship groups. Then, we obtain the optimal weighting vectors for each fuzzy-trend logical relationship group by using particle swarm optimization techniques to perform the forecasting. We also apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the NTD/USD exchange rates. The experimental results show that the proposed method gets higher average forecasting accuracy rates than the existing methods.

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