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.

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