本文討論在抽樣調查中被視為隨機集合模型的樣本，並試著架構基於模糊統計邏輯的粗化數據(coarse data)之理論與特性。因為有些抽樣調查中的數據可以視為隨機集合模型所得出的新數據。如何應用數學分析方法，配合軟計算技術以達到有效之資料處理與統計分析就是本研究之重點。我們將隨機抽樣樣本當作隨機實驗所做出來的結果，而這個論點可以幫助我們分析粗化數據。在探索抽樣調查的隨機集合和分佈的時候，機率測度論提供了很多種非精確數據給予統計學推測結論(statistical inference)，我們推廣傳統理論，以模糊集合及隸屬度為基礎，作為集合元素運算之依據。 關鍵字：粗化數據、隨機集合、隸屬度函數 / In this paper we discuss the sample in the random set model for the sampling survey. Since the data from sampling survey can be treated as a new type of data from the random set model. How to apply the mathematical analyzing methods as well as soft computing techniques to reach an efficient propose is our main goal. We treat random sampling data as the result of random experimental design. And this concept will help us to analyze the coarse data. Finally, in investigating the random set and its distributions for the random sampling survey, traditional probability measure theory serves an important role in the statistical inference, while we use the membership function and fuzzy operations to extend traditional concept into a more general case. Keywords： Coarse data, Random set, Membership function

在具有多變性、不確定性與訊息不完整的資訊網路時代，過去使用單一數值樣本來計算統計參數的方法，似乎已漸不符合現今多變與複雜的環境的需求。尤其在財金領域的資料採礦(data mining)研究中，利用模糊統計分析與軟計算方法，將會是一種更為接近實務需要的測度與估計工具。本研究提出模糊期望值的定義及一些相關性質，希望能配合隸屬度函數之觀念，將多元思維取代傳統二元邏輯的思考模式。並對複雜的財金問題，提出更符合人類社會行為及思考模式之實務探討。

應用模糊調查與統計方法去瞭解國中數學評量試題在教師與學生間以及學生不同背景（性別、對數學喜歡程度、課後數學練習時間及有無參加數學相關課外活動）對試題難易度的認知差異。結果顯示：在教師與學生之間、性別、學生對數學喜歡程度及課後數學練習時間方面有顯著差異，但是在參加課後數學相關活動方面對於數學科試題的難易度認知並沒有顯著的差異性存在。 / Using fuzzy statistical methods to understand whether the cognitive difficulty scales of the junior high school mathematics assessment questions shows difference between those given by teachers and students, by students with different genders, with different preferences, with different amounts of time spent on math practice after school, with participation or not in various math related seminars. Result demonstrates that significant difference between teachers and students, between students with different genders, between students with different preferences, and between students with different amounts of time spent on math practice after school. However, there is no significant difference between students with participation or not in various math related seminars.

在知識經濟之社會，多元思維逐漸取代傳統二元邏輯的思考與分析方法。過去使用單一數值的樣本來計算中位數的方法，已漸不符現今複雜多變的智慧科技時代之需求。尤其是在具有多變性、不確定性、與訊息不完整性的財金與經濟環境下，過分強調對於數值之運算及數學假設的前提，反而更容易造成與現實環境及條件的背離、甚至是脫節。故在進行財金與經濟方面問題的研究時，利用隸屬度函數與模糊統計的分析將會是一種較為進步的測度方法。本文在此提出模糊中位數的分析理論，並將其應用於財務金融的分析測度上，期望能對複雜的財金經濟現狀提供一套更有效且精確合理的分析方法。 / In the society of economic knowledge, Multi-valued logic goes to replace binary logic gradually. In the traditional way, we usually ask the task-taker to response the answer according to the thinking of binary logic. But such kind of response is improper since the human thinking is fuzzy and uncertain. So it should be an improved measurement using membership functions and fuzzy statistics. 　　In this paper, we will propose the definition of fuzzy median, and present some of its application. According to the above theoretical contents, we give some examples, which is used frequently in financial and economic assessment. From the explanation and discussion of fuzzy median in these examples, we can recognize that fuzzy statistics is more meaningful and proper for research of finance and economics. At last, based upon the findings of this study, certain recommendations for further research are suggested.

本文以人對事物現象認識的感覺與模糊性作為切入點，闡述模糊性是人對事物認識的一種表徵及反應。然後，引入模糊集合的定義及刻劃模糊集合的表示函數—隸屬度，對模糊集合的各種運算、模糊矩陣、模糊差集以及宇集等內容進行較詳細的討論，並以各種事例說明一些相關概念和運算。 最後，再深入探討如何以模糊矩陣表示圖學中有向圖的問題。 / This article is to focus on the understanding of human being to the phenomenon of things as well as the fuzziness. Then, by applying the definition of the fuzzy set and explaining the membership of fuzzy set, we are going to have a detailed discussion of the operation of fuzzy set, fuzzy matrix, fuzzy subtraction and universal set. Examples are given to demonstrate some of the related concepts and expression. Next, further questions about how to display directed graph in the graph theory with fuzzy matrix will be discussed .

石油是維持人類生存必需的商品，是容易運輸、儲存、使用的能源。石油價格的漲跌，將直接或間接影響經濟成長與物價水準。以公司營運來說，對海運業、航空業、石油公司等石油高度相關行業來說，購油成本一直佔據公司總成本相當大的比例，因此石油價格的變動，將使得會計年度內的購油成本高低相差甚大，進而影響公司整體營運利潤，因此購油決策重要性自不待言。當預測油價會上漲時，則公司將會以較低的石油價格購入較多的石油事先加以貯存或使用，以降低全年購油成本與分散風險。本文嘗試著導入模糊統計的概念並建立多變量多階自廻歸模糊時間數列模式，以期應用在油價之預測。實證方面則收集紐約商品交易所 (NYMEX: New York Mercantile Exchange) 的每日原油收盤價原始資料，針對原油價格進行模糊時間數列分析與預測，並比較命中率、誤差率與準確度。相信這對於購油風險控管及降低成本，提高公司盈餘深具意義。

Abstract In time series analysis, we often find the trend of dynamic data changing with time. Using the traditional model fitting can't get a good explanation for dynamic data. Therefore, many scholars developed various methods for model construction. The major drawback with most of the methods is that personal viewpoint and experience in model selection are usually influenced in them. Therefore, this paper presents a new approach on genetic-based modeling for the nonlinear time series. The research is based on the concepts of evolution theory as well as natural selection. In order to find a leading model from the nonlinear time series, we make use of the evolution rule: survival of the fittest. Through the process of genetic evolution, the AIC (Akaike information criteria) is used as the adjust function, and the membership function of the best-fitted models are calculated as performance index of chromosome. Empirical example shows that the genetic model can give an efficient explanation in analyzing Taiwan exchange rates, especially when the structure change occurs.

近幾年來，非線性時間數列轉折點的研究愈來愈受到重視，學者們也提出許多關於轉折點的偵測及檢定方法。若考慮實際資料走勢轉變的情形，“轉折區間”的概念更可以解釋結構改變的現象。但文獻中對於如何找尋時間數列結構改變之轉折區間的研究並不多。本文擬以時間數列統計模式及模糊學理論的角度來研究，並結合遺傳演算的規則而提出主導模式的概念，來架構出時間數列遺傳模式，再藉由轉折區間決策法則來找出數列的轉折區間。其中，我們以統計模式為遺傳演化過程中的染色體，而以候選模式之隸屬度函數為衡量染色體適應能力的指標。最後，我們舉出臺灣股價收盤指數之實例，分別以我們所提出的方法及其他方法找出數列的轉折區間及轉折點，並做比較。 / For recent years, the research of change point in nonlinear time series has been considered to be more and more important. Scholars have proposed a lot of detecting and testing methods about change points.If considering the trend of real situation, the concept of change period will show the phenomena of structure change.But there are not many researches about how to find change period in time series.My paper is based on the points of time series models and fuzzy theory.Besides,it combines the rules of genetic algorithm and provides the concepts of leading model to construct time seriep genetic model and to find out change period by decision rule.ln this paper, we use time series statistical models as chromosome in procedure of genetic evolution, and we also use membership function of selected models as pereformance: index of chromosome.Finally, the empirical application about change periods and change points detecting by our method and other's for Taiwan stock closing prices is demonstrated and make a comparision with these results.

模糊理論開始於 1960 年代中期,關於這方面的研究與發展均已獲得相當不錯的成果.其中尤以在群落分析應用上的專題研究更是廣泛.Bezdek 提出的模糊分類演算法,乃根據 Dunn 的C平均法所作的一改良方法.但仍有其缺點,例如,未考慮權重且以靜態資料為主. 有鑑於此,本研究對 Bezdek 之方法加以改進推廣,提出加權模糊分類法.對於評價因素為多變量時,應加入模糊權重的考量.此外更結合時間因素,使準則函數成為動態的模式,將傳統的模糊分類法由靜態資料轉為動態資料形式,以反映真實 的情況. / Research on the theory of fuzzy sets has been growing steadily since itsinception during the mid-1960s. The literature especially dealing with fuzzycluster analysis is quite extensive. But the research on FCM still has somedisadvantages. For instance, the

本文嘗試以模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊關係、模糊規則庫和模糊時間數列模式建構與預測等。我們首先給定模糊時間數列模式的概念與一些重要性質。接著提出模糊規則庫的定義，以及模式建構的流程，並以模糊關係方程式的推導，提出模糊時間數列模式建構方法。最後，利用提出的方法，對台灣地區加權股票指數建立模糊時間數列模式，並對未來進行預測，且考慮以平均預測準確度來做預測效果之比較。這對於財務金融的未來走勢分析將深具意義。 / The paper has attempted to apply the concept of fuzzy method on the analysis of time series. This reserch is also to include fuzzy relation, fuzzy rule base, fuzzy time series model constructed and forecasting. First, we'll define the concept of fuzzy time series model and some important properties. Next, the definition of fuzzy rule base will also be put forward, along with procedure of model constructed, the formation of fuzzy relation polynomial, and the methods to construct fuzzy time series model. At last, with the above methods, we'll build up fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. This shall carry profund signifigornce on the analysis of future trend in terms of financialism.