由於電腦革命的成功，在短暫的幾年之間，更加速了經濟的成長，而金融的投資分析，是社會經濟發展的原動力，因此研究這方向的財務數學也相對的提高了專家、學者的研究熱潮。就以股票、匯率市場來說，如果能比别人早一步掌握行情走勢，就能獲得較高的利潤。但影響股價、匯率波動的因素很多，尤其是在複雜多變及不確定性的資訊下。因此；如何進行更精確的趨勢分析與預測，是本文研究的主題。由於，傳統的期望值是二元的邏輯思考(非1即0)，比較無法符合多變與不確定的財金問題，因此本文考慮以模糊統計方法，以模糊期望值的方法來作趨勢分析與預測，期望能對複雜多變的財金體系提共一套更精確合理的投資分析方法，可以提供投資者更多的訊息，做出明確的抉擇。最後；以我國集中市場加權股票指數、台幣對美元匯率及台積電股價為例，做一實例上的詳細探討。 / Based on computer revolutionary coming off, economics grows fast in previous several years, then the investment analyze of finance is the impetus of development of society economic. Therefore, many experts and scholars are interested in the research of financial mathematics. Taking stock market and exchange market for example, if you can predict the future trend of market, you obtain more profit. However, there are many factors that act on stock prices and exchange rate. Especially, the market information is complicated and incomplete. How to go along accurate trend analysis and divination is the important point of the text research. Because traditional expectation value is dibasic logic thought (either 1 or 0), that can’t conform to the highly changeable and uncertain finance problems. For this reason, in this research we propose an integrated procedure for fuzzy expectation value modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy expectation value model for Taiwan Weighted Stock Index and exchange rate and forecast future trend. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

波浪理論是由 Nalph Nelson Elliott在1938年所發表的價格趨勢分析工具，它也是近年來技術分析界運用相當廣泛的一種工具。艾略特認為：「不管是股票或是任何商品價格的波動，都與大自然潮汐一樣，具有一種相當程度的規律性。」。其實這個原理和產業周期循環也很接近，運用於越多人參與的市場會越準確，因為人性也是一種大自然的現象。 台灣加權股價指數是以民國55年為基期100來編製，本文雖由民國55年談起，但由於資料繁多，故集中採用民國76年1月至民國95年12月的二十年資料做為資料收集期間，以艾略特波浪理論的原則找出在台灣股市的應用規則，進而推演出未來的走勢。 / Wave Principle is a trend analysis method that was developed by Nalph Elliott in 1938. Today, the principle is one of the most widely adopted methods for technical analysis in finance. Elliott discovered that the ever-changing path of stock market prices reveals a structural design that in turn reflects a basic harmony found in nature. In fact this principle is also similar to industry cycle. When this principle is utilized in a market, especially when a lot of people participate in this market, the principle will be rather accurate, because humanity is also a natural phenomenon. The Taiwan Weighted Stock Index was at 100 in 1966, the base period. Although the discussion in this paper starts from 1966, due to the abundance of the data, I decide to focus my research on the recent twenty years. The purpose of this study is to identify the usability of Eilliott’s Wave Principle by applying it in Taiwan’s stock market and to figure out the trend for the future.