本文的主要目的是為使用者建立一個方便使用及減少成本的網路問卷模型，以模糊統計為基礎，主要探討梯形隸屬度函數的統計量，讓使用者能透過系統，從事問卷調查。 網站共有5個部份,分成(1)問卷調查(2)威克生等級檢定(3)離散型模糊資料統計量(4)連續型模糊資料統計量(5)模糊迴歸；網頁使用ASP.NET2.0撰寫，並在其中加入資料庫語法，連結資料庫，讓使用者可以在線上輸入資料，並獲得統計結果。 / The main purpose of this paper is to build up a questionnaire model, which is convenient to use and can reduce cost for the users. With the foundation of the fuzzy statistics, the main study is about the statistical quantity of trapezoid membership function, and let them work on a questionnaire through system. The website totally has 5 parts and is divided into (1) A questionnaire, (2) Wilcoxon Signed-Rank Test, (3) The statistical quantity with discrete fuzzy data, (4) The statistical quantity with continuous fuzzy data, (5) Fuzzy regression equation. The web page is composed of ASP.NET2.0, and database phrasing is added therein to link database. Let users input data on line, and get the results of statistics.

在時間數列的分析上，由於一些辨識模型結構的方法，常受制於時間數列本身的非定態及不確定干擾的影響，因此若以單一模式來配適數列往往不能得到滿意的結果。 此外，傳統的統計方法太依賴數字本身，但當一時間數列其資料呈相當的模糊性時，我們往往僅對其走勢感興趣，故若能從圖形識別的觀點，找出與此時間數列具有高度相似性的資料，以作為此時間數列的領先指標或參考指標，應可比傳統單一時間數列模式（無論是線性或非線性）更能解釋資料走勢及解決結構性改變之問題，並能夠即時反應最丟出伏況，增加預測之準確性。 在本文中，我們考慮應用模糊理論建立一時間數列模糊相似性演算法 ，來辨識時間數列之間的相似性。在執行此演算法的過程申，我們依資料的特性如變異數是否改變、是否有離群值或突發值干擾等的不同，提出值域均分法、k-means值域均分法及Rank轉換法等三種方法來建構隸屬度函數 ，以求得對資料更好的解釋及預測結果。模擬的結果顯示 ，值域均分法在時間數列間的模糊相似性辦識表現最好。而在實證分析中，我們以此演算法來辨別GDP與民間消費、GDP與毛投資之間的模糊相似性，其結果相當不錯。 / An important problem in pattern recognition of a time series is similarity recognition. This paper presents the methods of similarity calculation for two time series. The methods considered include equally divided range method, K-rneans method and rank transformed method. The success of our similarity recognition relies a large extent on the fuzzy statistical concept. Simulation results demonstrate that, overall, the equally divided range method performed best in the similarity recognition. While other methods provide superior efficiency in calculating similarity for certain special time series. Finally two empirical examples, similarity calculating about GDP vs. Consumption and GDP vs. Invest, are illustrated.

現今對於幸福感此一主題的測量，主要採用自陳量表的方式。然傳統量表無法精確描述人類多元行為，為期能更正確的瞭解受訪者的內在感受與想法，因此本研究提出模糊統計模式，期能針對過去傳統自陳量表之不足予以改進。而校長身為一間學校的領導者與管理者，其幸福感之程度，必會對學校的氣氛與發展產生直接或間接地影響。雖目前對於教師幸福感及學生幸福感的研究頗多，但針對校長職業幸福感之研究迄今仍尚付闕如，是故此主題值得深究。 本研究採用問卷調查法，以北北基地區國中校長共50位為對象，採用「中學校長職業幸福感量表」為工具，並以敘述統計、偏最小平方法、曼－惠特尼 U 檢定、克－瓦單因子等級變異數分析、Pearson積差相關分析、模糊統計等統計方法進行分析。主要研究結果如下： 1. 北北基地區中學校長對職業幸福感的知覺與感受程度屬中高程度，以「內心滿足感」最高，「職業成就感」居次，最後為「職業滿意感」構面。 2. 服務年資在1-8年的校長的「職業幸福感」高於服務8年以上之校長。 3. 任職「國民中學」的校長其「職業幸福感」高於任職「完全中學」的校長。 4. 模糊語意尺度所得之信度與建構效度均優於傳統問卷尺度所得。 本研究根據資料分析結果進行討論，並提出數點建議供後續相關工作及研究參考。 / Well-being of principals is one of the most important indicators of a school. Principals as leaders and managers in schools, their condition of well-being can directly or indirectly affect the atmosphere and development of schools. The most common measurement regarding the topic is self-report inventory, However, traditional inventories cannot reflect human’s behaviors. In order to clearly understand interviewees’ feelings and thoughts, the study provided fuzzy statistics model in the hope of improving insufficiencies of traditional inventories. In the study, a questionnaire survey method is used, and 50 principals from Taipei-Keelung metropolitan area are surveyed with stratified sampling. Data analysis includes descriptive statistics, PLS-SEM, Mann–Whitney U test, Kruskal-Wallis one-way ANOVA by ranks, Pearson product–moment correlation analysis, and fuzzy statistics. The main conclusions are as follows: 1. The occupational well-being of principals from Taipei-Keelung metropolitan area was above the medium level. “Inner satisfaction” factor was the highest score on “occupational well-being”. 2. The principals with 1-8 years of service, their occupational well-being was better than the principals who have 8 or more years of service. 3. The occupational well-being of principals in junior high school was better than the principals in complete high school. 4. The reliability and construct validity calculated by fuzzy scales were better than by traditional scales. This research mainly focuses on the data analysis and discussion, and provides some suggestions for future studies.

近年來，民意調查有廣泛使用在預測競選期間選情動向的趨勢，試將問卷設計為探討選民們投票理念與投票行為意圖，以預測選民投票意向。但現實社會裡，並不能以二元邏輯的觀念來劃分人類的思想理念與行為意圖，因為人類的思維、決策、行為中都包含模糊不確定性與非定量化的特質，即集合中元素的隸屬度假若是模糊不確定的，非完全屬於此集合又非完全不屬於此集合，則二元邏輯觀念可能無法詳盡地探訴事件本身所具代表的真相，將會扭曲它背後隱藏的因素意義，故欲應用多元邏輯更精確地描述人類不確定性的模糊特質。 本論文將職務表現、政治形象、候選政見、所屬政黨列為預測台北市長選舉的探究因素，應用模糊統計分析傳統問卷，認為每一位選民將因本身的獨特因素特徵，各視影響選情的論域有著不盡相同重要程度，故考慮個體模糊權重、總體模糊權重、模糊權重數的選定，評定三位台北候選人將各具有不同程度的隸屬函數，利用隸屬度與決定投票意向之間的微妙關係，以最大隸屬度預測選民最終決定的投票意向，將對複雜的選舉情勢作更適合的預測估計。 / Public opinion survey has played an important role and has been utilized in forcasting an election campaign. Trying to get an unbiased and reliable forcast that best explain voters behavior, researchers have put a tremendous effort in designing the survey questions trying to capture the true essence of voters intention and action. In this paper, we apply logic of fuzzy theory to extract the voters inclination to vote for any candidate in the event of uncertainty surrounding the voters that may affect his or her voting decision. This paper has taken into account of candidate performance, public image, political views and political party as discussible factors that many have inflected the process of Taipei mayoral election. Furthermore, we use individual fuzzy weight, total fuzzy weight and fuzzy weight to assign the membership function to the candidates. The candidate who has obtained the maximum membership function based on the above categories is likely to get the vote from the uncertain votes.

Many papers have been presented on the study of change points detection.　Nonetheless, we would like to point out that in dealing with the time series with switching regimes, we should also take the characteristics of change periods into account.　Because many patterns of change structure in time series exhibit a certain kind of duration, those phenomena should not be treated as a mere sudden turning at a certain time. In this paper, we propose procedures about change periods detection for nonlinear time series.　One of the detecting statistical methods is an application of fuzzy classification and generalization of Inclan and Tiao’s result.　Moreover, we develop the genetic-based searching procedure, which is based on the concepts of leading genetic model.　Simulation results show that the performance of these procedures is efficient and successful.　Finally, two empirical applications about change periods detection for Taiwan monthly visitors arrival and exchange rate are demonstrated.

中華民國第十任總統選舉結果於民國八十九年三月十八日揭曉，這場眾所矚目的選舉終告落幕，然而對選舉研究工作者而言卻是新的開始。選舉預測居選戰中重要的一環，也是研究選舉的學者關心的問題，更提供了一個驗證選民投票行為理論的絕佳機會，近來國內相關論述已有相當成果。但由於它在投票結束，便有答案，其挑戰程度不言而喻。因此，如何結合理論、方法及事實三者為一體的努力，對選舉預測更是別具意義。 本篇研究之範圍，是以公元2000年總統大選為例，對選舉預測工作做更深層的探討，且檢驗邏輯斯預測模型（Logistic Regression Model）及模糊統計（Fuzzy Statistics）分析在本次總統選舉的預測力，考量本次總統選舉中各項可能影響選情的因素，進一步建構選舉預測模式，然而兩種預測模式的初步預測結果並不佳，經過棄保效應的可能性調整後，預測誤差已大幅降低，其中模糊統計（Fuzzy Statistics）分析預測結果經棄保效應調整後，與實際開票結果相當接近，因此與邏輯斯預測模型相較，模糊統計分析的應用對未表態選民投票意向的預測力較佳。一套完整的選舉預測模型研究，應包含問卷設計、抽樣訪問、資料處理、加權除錯、模型設計與預測評估等整套研究流程，然而在本次總統大選中，由於三強激戰，影響選情因素相當複雜，最後此兩種選舉預測模式皆無法獲致精確的預測結果。因此，我們期待選舉預測模型的建構，能突破主客觀環境的侷限，進一步達到「準」與「穩」的要求。 / With the successful staging of the 2000 presidential elections in Taiwan, scholars have been presented with a new opportunity to test their theories. Electoral predictions are an important field within the study of elections and have been among the most keenly studied questions over the past few years. Unlike many other research topics, there is an absolute standard for election predictions: the election results. Thus, combining theory, methodology, and facts to obtain a meaningful result is no simple task. This thesis attempts to predict the 2000 presidential election using both a logistic regression model and a fuzzy statistics model. After constructing models which includes all kinds of different variables that might influence the electoral outcome, we find that neither the logistic regression model nor the fuzzy statistics model is particularly accurate. However, after accounting for the effects of strategic voting, model error decreases dramatically. In particular, after including provisions for strategic voting, the fuzzy statistics model is improved to the point that its predictions are extremely close to the actual outcome. Thus, we show that the fuzzy statistics model is superior to the logistic regression model in analyzing the vote choices of undecided voters. Research on electoral predictions should include such aspects as questionnaire design, sampling, interviewing, data processing, weighting, data cleaning, model design, and evaluation of the prediction. However, because this election featured a particularly intense three way race, the factors affecting the electoral outcome were both numerous and intertwined in complex ways. Unfortunately, it is impossible to evaluate our electoral predictions of the two models precisely. We hope that in the future, election prediction models will be able to break through these environmental limitations and achieve more accurate and stable predictions.

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.

試題難易度評量一直是許多人研究的課題。但傳統方法的五點量表問卷只提供固定尺度的選擇，似乎無法完整地表達受測者真實且複雜的思考。因此本文將以模糊問卷調查進行試題難易度的探討。許多研究應用模糊平均數、模糊眾數或模糊中位數等概念於試題難易度評量。而本文將以此為基礎，定義一種新的距離，再透過一些轉換取得試題的難易度指標，進而比較各試題之間難度的差異。本文的另一個重點，是各個不同難度因子的向度來決定各試題的難度。再以模糊相對權重的概念，對各向度的難易度指標作加權，進而比較、分析。 / Assessment for test difficulty have been the subject of many studies. The traditional method of a Likert scale questionnaire provides only a fixed scale choice, but it seems that we can’t fully express the real and complex thinking of respondents. Therefore, the thesis will apply fuzzy questionnaire to probe into test difficulty. Concepts such as Fuzzy mean, Fuzzy mode or Fuzzy median are applied in studies of assessment for test difficulty. The thesis will be based on these conceptions to define a new distance, and obtain the difficulty index of test through some conversion. Moreover, it will compare the differences of difficulty among test items. Another focus of this paper is to determine the difficulty of each item according to various dimensions of difficulty factors. Afterwards, the difficulty index of each dimension will be weighted, compared, and analyzed with the concept of fuzzy relative weight.

兩變數之間是否相關，以及相關的程度與方向是統計研究學者所關注的一項課題。傳統上使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩實數變數間線性關係的強度與方向。然而，對於反映人類思維不確定性的模糊資料而言，傳統的相關分析方法卻有不足與不適用之缺失。 　　本論文的主要目的在於尋求一個合理、適用的區間模糊資料相關係數，提供研究者簡單且容易計算的模糊相關係數求法，用以了解區間模糊資料間的相關程度。接著利用轉換離散型模糊數成為區間模糊數的方式，處理離散型模糊資料間的相關係數。最後，以國中數學教學現場所調查的資料做實例應用。 / In statistical studies, the correlation between two variables and its strength and direction are always concerned. Traditionally, the Pearson’s Correlation Coefficient is used to convey the linear relationship between two variables. However, the traditional correlation analysis is not applicable to the fuzzy data which are able to reflect more appropriately the uncertainty of human thinking. 　　The main purpose of the study is to find a reasonable and usable correlation coefficient of interval fuzzy data which provides researchers a simple and easy way to calculate and find the fuzzy correlation coefficient. Meanwhile, it can help us understand the correlation of interval fuzzy data. Moreover, we use the process of transforming discrete fuzzy number into the interval fuzzy number to deal with the correlation coefficient of discrete fuzzy data. Finally, we utilize the data from mathematics teaching in junior high school for application.

在試題難易度分析上，傳統方式常以答對率或得分率的高低來認定試題的難易度。但答對率或得分率高低並不能真正表達應試者在答題時的難易感受程度。過去研究指出影響數學科試題難易度的主要因素有三：評量的數學內容、解題時的思考策略及解題所需的步驟數。 本論文針對影響數學科試題難易度的三個主要因素進行分析統計。以模糊統計的角度，提出非固定權重因子之二維模糊數。應用模糊數絕對距離的概念以摒除族群中異端值，最後針對不同族群進行難易指標分析與檢定。 / On the basis of difficulty analysis, the hit rate or the scoring rate are considered as the index of the difficulty of the questions traditionally. However, these rates can not represent how test takers feel when taking tests. According to the previous papers on this subject, they note three factors to affect the difficulty analysis on math questions the content of the evaluation, the strategies of question solving, and the required steps to solve a question. This research is focused on the three major factors which influence the difficulty of math examinations. With the angle of fuzzy statistics, a two-dimension fuzzy number will be presented with non-fixed weighted factors. By applying the absolute distance concept of fuzzy number, the extreme values are excluded. Consequently, the indices of difficulty from different groups can be tested and analyzed.