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In this paper, we present a new method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series, where the main factor is the TAIEX and the secondary factors are either the Dow Jones, the NASDAQ, the M1b (Taiwan), or their combinations. First, we fuzzify the historical data of the main factor into fuzzy sets with a fixed length of intervals to form fuzzy logical relationships. Then, we group the fuzzy logical relationships into fuzzy logical relationship groups. Then, we evaluate the leverage of fuzzy variations between the main factor and the secondary factor to forecast the TAIEX. The experimental results show that the proposed method gets a higher average forecasting accuracy rate than Chen's method  and Huarng et al.'s method  to forecast the TAIEX.