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研究生:邱清爐
研究生(外文):Chin-Lu Chyu
論文名稱:模糊迴歸分析中最小平方法之求解與應用
指導教授:高強高強引用關係
指導教授(外文):Chiang Kao
學位類別:博士
校院名稱:國立成功大學
系所名稱:工業管理科學系碩博士班
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:92
中文關鍵詞:擴展法則最小平方法迴歸分析模糊集合人力資源管理
外文關鍵詞:Fuzzy SetsRegression AnalysisLeast-squares MethodExtension PrincipleHuman Resource Management
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摘 要

迴歸分析為一重要的決策分析工具,其主要目的在於探討解釋變數與反應變數之間的特定關係,並據此關係以進行預測。由於現實環境中,有些資料具有模糊現象,致使傳統的分析方法難以使用。在Bellman與Zadeh提出模糊理論的概念後,許多學者便將迴歸分析方法擴展至模糊環境中,以做更廣泛的應用。但是,在現有模式中,其共同特點為求解的迴歸係數為模糊數值,以致於在進行反應變數的估計時,估計值的展度(spread)會隨解釋變數數值的增加而擴大,因而降低了模式的應用性。
本研究提出最小平方法的概念,以建構模糊資料的迴歸模式。其觀念乃基於Zadeh的擴展法則(extension principle),直接推導誤差平方和的隸屬函數。由於誤差平方和為迴歸係數的函數,故接著利用Chen與Klein的模糊排序方法,透過一組最小化的非線性規劃問題求解迴歸係數。由於所求解的迴歸係數為明確數值,除了反應變數與解釋變數之間的關係可以精確獲得之外,並可避免先前文獻的共同缺失,使決策者得以提升其決策品質。
本研究除了發展模糊迴歸模式的求解方法之外,文中亦對模糊相關係數與模糊判定係數的衡量方法以及模糊迴歸模式的選擇進行探討。本文最後以台灣的勞動市場為例,分析失業率、學用相關性與工作滿意度之間的關係,以說明在口語化述詞資料的情形下,如何將模糊迴歸分析應用於人力資源管理問題。

關鍵詞:模糊集合、迴歸分析、最小平方法、擴展法則、人力資源管理
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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