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 Abstract Regression analysis is a powerful and comprehensive methodology for investigating the relationship between a response variable and a set of explanatory variables. Inferential problems associated with the regression model include the estimation of the regression coefficients and prediction of the response variable from knowledge of the explanatory variables. In practice, there are cases that the observations are fuzzy in nature which would make the classical regression model not applicable. Since the fuzzy set theory proposed by Bellman and Zadeh, several scholars have constructed different fuzzy regression models and proposed the associated solution methods for wider applications. Previous studies on fuzzy regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the explanatory variable increases its magnitude, which is not suitable for general cases. In this thesis an idea stemmed from the classical least squares is proposed to handle fuzzy observations in regression analysis. Based on the extension principle, the membership function of the sum of squared errors is constructed. The fuzzy sum of squared errors is a function of the regression coefficients to be determined, which can be minimized via a nonlinear program formulated under the structure of the Chen-Klein method for ranking fuzzy numbers. Since the regression coefficients are crisp, the problem that the spreads in estimation are increasing suffered by the previous studies can be avoided. How to measure the correlation coefficient and coefficient of determination under fuzzy environment is also discussed in this thesis. To select an appropriate model with better fit of the observed data is desired by the decision-maker. A methodology to achieve this end is proposed as well. Finally, the relationship between job satisfaction, as the response variable, and unemployment rate and job relevancy, as two explanatory variables, of Taiwan college graduates are investigated to illustrate the advantage of the proposed fuzzy regression model.Keywords: Fuzzy Sets, Regression Analysis, Least-squares Method, Extension Principle, Human Resource Management.
 目 錄中文摘要……………………………………………………Ⅰ英文摘要……………………………………………………Ⅱ誌謝…………………………………………………………Ⅲ目錄…………………………………………………………Ⅳ表目錄………………………………………………………Ⅵ圖目錄………………………………………………………Ⅶ第一章 緒論……………………………………………… 1 第一節 研究動機與目的……………………… 1 第二節 研究方法與進行步驟………………… 3 第三節 相關研究……………………………… 5第二章 最小平方法………………………………………11 第一節 求解方法………………………………12 第二節 模糊誤差估計值………………………17 第三節 本章數值範例…………………………18 第四節 討論……………………………………33第三章 統計性質分析……………………………………35 第一節 模糊相關係數…………………………35 第二節 模糊迴歸模式的變異數分析…………38 第三節 模糊判定係數…………………………41 第四節 本章數值範例…………………………42 第五節 本章結論………………………………51第四章 模糊迴歸模式的選擇……………………………53 第一節 模式選擇的必要性……………………53 第二節 各種模糊迴歸模式的建構與評估……54 第三節 本章數值範例…………………………56 第四節 討論……………………………………62第五章 工作滿意度實例應用……………………………66 第一節 失業率、學用相關性及工作滿意度…66 第二節 口語化述詞的資料轉換………………68 第三節 資料實證結果…………………………70 第四節 本章結論………………………………73第六章 結論………………………………………………75參考文獻……………………………………………………77自述…………………………………………………………84表 目 錄表 2-1 範例2-1中的數值資料與估計誤差……………20表 2-2 範例2-2中的數值資料與估計誤差……………25表 3-1 範例3-1中不同 截集下模糊相關係數與模糊判定係數的上下限值 ……………44表 3-2 範例3-1中不同 截集下三種模糊平方和的上下限值 ………45表 3-3 範例3-2中不同 截集下模糊相關係數與模糊判定係數的上下限值 ……………48表 3-4 範例3-2中不同 截集下三種模糊平方和的上下限值 ………49表 4-1 範例4-1中五種模糊迴歸模式在不同 截集下誤差平方和的上下限值 …………57表 4-2 範例4-1中五種模糊迴歸模式的估計誤差……58表 4-3 範例4-2中五種模糊迴歸模式在不同 截集下誤差平方和的上下限值 ……… 60表 4-4 範例4-2中五種模糊迴歸模式的估計誤差……62表 5-1 七個學門的失業率、學用相關性與工作滿意度 ……………70圖 目 錄圖2-1 反應變數觀察值與估計值隸屬函數之間的差異……………… 19圖2-2 範例2-1中三種模糊迴歸模式的誤差平方和之隸屬函數…… 21圖2-3 範例2-1中最小平方法所求得之模糊線性迴歸模式………… 24圖2-4 範例2-2中三種模糊迴歸模式的誤差平方和之隸屬函數…… 26圖2-5 範例2-2中最小平方法所求得之模糊線性迴歸模式………… 29圖2-6 範例2-3中最小平方法求解的誤差平方和之隸屬函數……… 31圖2-7 範例2-3中最小平方法所求得之模糊線性迴歸模式………… 32圖3-1 範例3-1中模糊相關係數的隸屬函數………… 44圖3-2 範例3-1中模糊判定係數的隸屬函數………… 45圖3-3 範例3-1中三種模糊平方和的隸屬函數……… 46圖3-4 範例3-2中模糊相關係數的隸屬函數………… 48圖3-5 範例3-2中模糊判定係數的隸屬函數………… 49圖3-6 範例3-2中三種模糊平方和的隸屬函數……… 50圖4-1 範例4-1中五種模糊迴歸模式的誤差平方和之隸屬函數…… 57圖4-2 範例4-1中五種模糊迴歸模式的趨勢線……… 59圖4-3 範例4-2中五種模糊迴歸模式的誤差平方和之隸屬函數…… 61圖4-4 範例4-2中五種模糊迴歸模式的趨勢線……… 63圖5-1 五個口語化述詞的模糊數值………………… 69圖5-2 工作滿意度分析中誤差平方和之隸屬函數…… 72圖5-3 工作滿意度的估計值…………………………… 73
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 1 以模糊理論分析BOT計畫自償率之研究 2 試題反應理論應用於試題之適性評量研究－以93年國中基本學力測驗國文科試題為例 3 應用灰色理論於匯率預測之研究 4 大學資管系女性畢業生生涯規劃與發展之研究－以南部某大學資管系為例 5 建築工程設計與施工作業介面在設計規劃階段之研究 6 台灣國際航空貨運量之預測 7 應用模糊資料包絡迴歸分析法於國內物流業經營績效之研究 8 模糊迴歸與傳統迴歸應用於估計潛在特質之模擬比較分析研究 9 模糊迴歸模式之建立及其應用─以橋面版劣化預測為例 10 模糊評量方法與傳統評量方法之相關研究－以國中基本學力測驗成績為例 11 求解模糊迴歸之參數估計 12 以類模糊羅吉斯迴歸預測企業違約之研究 13 較具有解釋能力之模糊線性迴歸模式 14 模糊理論應用於寡占市場之研究 15 影響台灣半導體製造業經營績效因素之研究

 1 17. 陳春盛、林鏡榮，「台灣北部地區大地起伏加密研究」，測量工程，第三十五卷，第四期，第37-46頁（1993）。 2 9. 吳究，「衛星定位電波相位量測與大氣效應之研究」，中國土木水利工程學刊，第四卷，第二期，第127-138頁（1992）。

 1 大量資料集之線性迴歸模式的估計問題 2 台灣高科技產業經營績效與其對大陸投資規模之研究 3 特徵價格理論之應用：澳洲葡萄酒之分析 4 具不精準資料之網路生產系統效率評比-以臺灣成衣製造公司為例 5 利用模糊目標規劃法求解田口式多品質特性最佳化問題 6 感應電動機之模糊類神經網路控制器之研究 7 儲料位置選擇之模糊層級分析決策方法應用-中鋼公司為例 8 模糊需求下批量訂購存貨模式之分析 9 模糊資料包絡分析模式之求解與應用 10 策略性人力資源、組織文化與組織績效之關係---以金融業為例 11 資源共享、企業控制策略與人力資源管理控制的角色:台灣集團企業子公司的實證研究 12 台灣高科技電子產業員工工作壓力與身心健康之探討：兩個工作壓力模型－Karasek「負荷控制支持」模型與Siegrist「付出回饋失衡」模型－之檢驗 13 台灣上市上櫃航運公司外匯風險暴露之研究 14 結合模糊理論於濁水溪流域逕流預報模式之研究 15 以不同統計模型分析基因型與環境交感效應之研究

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