| Summary: | 博士 === 國立成功大學 === 工業管理科學系碩博士班 === 90 === 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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