In this thesis, we propose a new fuzzy forecasting method for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the NTD/USD exchange rates based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization (PSO) techniques using optimal partitions of intervals in the universe of discourses and optimal weighting vectors of fuzzy-trend logical relationship groups. First, the proposed method uses PSO techniques to find the optimal partitions of intervals in the universe of discourses and the optimal weighting vectors of fuzzy-trend logical relationship groups based on the historical training data. Then, based on the obtained optimal partitions of intervals in the universe of discourses, it fuzzifies the historical testing datum of the main factor and the secondary factor on each trading day into fuzzy sets, respectively. Finally, based on the trend between the subscripts of the fuzzy sets of the fuzzified historical testing data of the previous two trading days of the main factor and the trend between the subscripts of the fuzzy sets of the fuzzified historical testing data of the previous two trading days of the secondary factor, it chooses the corresponding fuzzy-trend logical relationship group to perform the forecasting based on the obtained optimal weighting vector of the chosen fuzzy-trend logical relationship group. The experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods for forecasting the TAIEX and the NTD/USD exchange rates.

In this thesis, we propose a new fuzzy forecasting method for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the NTD/USD exchange rates based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization (PSO) techniques using optimal partitions of intervals in the universe of discourses and optimal weighting vectors of fuzzy-trend logical relationship groups. First, the proposed method uses PSO techniques to find the optimal partitions of intervals in the universe of discourses and the optimal weighting vectors of fuzzy-trend logical relationship groups based on the historical training data. Then, based on the obtained optimal partitions of intervals in the universe of discourses, it fuzzifies the historical testing datum of the main factor and the secondary factor on each trading day into fuzzy sets, respectively. Finally, based on the trend between the subscripts of the fuzzy sets of the fuzzified historical testing data of the previous two trading days of the main factor and the trend between the subscripts of the fuzzy sets of the fuzzified historical testing data of the previous two trading days of the secondary factor, it chooses the corresponding fuzzy-trend logical relationship group to perform the forecasting based on the obtained optimal weighting vector of the chosen fuzzy-trend logical relationship group. The experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods for forecasting the TAIEX and the NTD/USD exchange rates.

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