模糊語意量表的語意模糊數建構演算與實證分析

The Construction of Fuzzy Linguistic Numbers for Questionnaire and Its Empirical Study

林原宏(Yuan-Horng Lin)

《調查研究》 11期 (2002/04) Pp. 31-71

https://doi.org/10.7014/TCYC.200204.0031

摘要

本研究旨在以模糊集群（fuzzy cluster）之目標函數演算法（objective function algorithm），建立模糊語意量表之模糊數參數。傳統上常用李克特式量尺（Likert scale）或語意差異量尺（semantic differential scale）等量化方式，來衡量欲研究對象的心理與認知，且將語意變數（linguistic variable）量化為明確值（crisp value）之等距變數（interval variable）。但這種計分方式尚存有疑慮，要求填答者以「非此即彼」的二分法來選擇語意，並不符合人類在察覺（perception）判斷過程中，具模糊性、主觀性且不確定的特色。鑑於傳統李克特式量尺或語意差異量尺的量化計分的不妥之處，有部份的研究基於模糊理論（fuzzy theory）觀點，採模糊語意量表的設計與量化，而此方面的應用研究大部分均顯示，此量化方法頗能貼切地呈現填答者內心的感受。模糊語意量表的計量常採模糊數（fuzzy number）的方式，但量表的語意模糊數參數類型為何，卻欠缺合理的依據和適當的演算程序。所以，如何根據填答者的反應資料，建構適當的語意模糊數，是一個值得探討的問題。基於此，本研究以「教師信念量表」為例，將傳統的李克特氏量表增加改編設計為模糊語意問卷的填答方式，並利用模糊隸屬度加權（fuzzy membership weight）所得的填答者反應資料，以模糊集群之目標函數演算法，建立每一題的模糊語意之三角模糊數參數。根據本研究所建構的模糊數，嘗試分析傳統計分和模糊語意量表計分，並比較其在量表信度與效度之差異。根據實證資料分析顯示，模糊語意計分之信度與效度較傳統計分為佳，可知利用模糊集群的目標函數的演算法，所建立模糊語意之模糊數，可供後續進一步應用與研究之參考。

關鍵字

二元邏輯 ； 李克特式量表 ； 模糊理論 ； 模糊語意變數

並列摘要

The purpose of this study is to construct fuzzy numbers of questionnaires by objective function algorithm. In the traditional research method, we often investigate the latent traits of people by means of Liker scale or semantic differential scale. From the relative research finding, there are two problems worthy of discussing. The first one is that it is lack of reasons to transform linguistic variables into crisp and interval values. The other one is that the process of thinking is multi-logic in nature, which is quite different from the binary-logic assumption of traditional questionnaires. There are some literatures based on fuzzy theory to dissolve the above questions. According to most of these literatures, they reveal that the fuzzy logic is appropriate for questionnaire-design and the data analysis. As to the fuzzy linguistic variables, we often record them into fuzzy numbers. On the contrary, there are few researches discussing how to construct the corresponding fuzzy numbers of items. In this paper, 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”. The fuzzy numbers of each item are also defuzzified into real values for the purpose of scoring. By three different kinds of scoring, we can realize the reliability and validity of fuzzy linguistic scoring are better than those of traditional scoring. In the real data analysis, we can also realize that the fuzzy linguistic variables are proper for measuring latent trait. Finally, based upon the findings for this study, some recommendations for further research are suggested.

並列關鍵字

binary logic ； fuzzy linguistic variable ； fuzzy theory ； Likert scale

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