量表語意模糊數演算及其計分比較分析

The Algorithm of Fuzzy Linguistic Numbers and Its Comparison of Scoring

10.7037/JNTTC.200312.0279

林原宏(Yuan-Horng Lin)

二元邏輯 ； 李克特式量表 ； 模糊理論 ； 模糊語意變數 ； binary logic ； fuzzy linguistic variable ； fuzzy theory ； Likert scale

臺中師院學報

17卷2期（2003 / 12 / 01）

279 - 304

繁體中文

本研究旨在探討量表的傳統計分和模糊語意計分之特性，研究者以實證資料和資料模擬兩方面，在有無「解模糊化」和「模糊隸屬度加權」的情形下，分析比較傳統計分和三種模糊語意計分之信度與效度差異。 在實證資料方面，以模糊集群（fuzzy cluster）之目標函數演算法（objective function algorithm），建立模糊語意量表的模糊數參數，並將模糊數解模糊化以供計分之用。實證資料的分析中，顯示模糊語意計分的信度比傳統計分為高，且模糊語意計分中，以兼具「解模糊化」和「模糊隸屬度加權」的計分方式Ⅲ之信度與效度最高。 在資料模擬方面，以題數、人數和潛在特質分配型式為因子設計，分別比較傳統計分和三種模糊語意計分之信度差異。模擬結果與實證分析相同，亦即模糊語意計分的信度比傳統計分為高，而三種模糊語意計分中，亦以兼具「解模糊化」和「模糊隸屬度加權」的計分方式Ⅲ之信度最高。 根據本研究實證和模擬所獲得的一致性結果，顯示模糊語意計分有其應用與發展之處。而本文利用模糊集群的目標函數演算法，所建立模糊語意之模糊數，亦可供後續進一步應用與研究之參考。最後，本文根據研究結果，提出未來進一步研究和應用發展之建議。

The purpose of this study is to evaluate the reliability and validity of fuzzy linguistic variables. By the method of empirical study and data simulation, we will realize the characteristics of three kinds of fuzzy scoring. In the empirical study, the objective function algorithm of fuzzy cluster is used to calculate the parameters of fuzzy numbers and the empirical data set is gotten from the questionnaire of “The Teacher Faith Scale.” For the purpose of fuzzy scoring, the fuzzy numbers are defuzzied. Form the results of Cronbach’s reliability, it shows that there is difference between traditional scoring and fuzzy scoring. The Cronbach’s reliability and validity of fuzzy scoring is larger than that of traditional scoring. In addition, there is also difference among three kinds of fuzzy scoring. As for the fuzzy scoring, when the “defuzzification” and “weighted membership” are considered, the Cronbach’s reliability and validity of this kind is the highest. Moreover, in the study of data simulation, the factors contain “number of items”, “number of task-takers”, and “distribution of latent.” According to the comparisons of the Cronbach’s reliability, the results of data simulation was similar to those of empirical study. It also appears that Cronbach’s reliability of fuzzy scoring is larger than that of traditional scoring. The factors, “defuzzification” and “weighted membership”, will prompt the reliability of fuzzy scoring. From results of empirical study and data simulation, we can realize that the reliability and validity of fuzzy linguistic scoring are better than those of traditional scoring. Finally, based upon the findings of this study, some recommendations for further research are suggested.

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