試題難易度評量一直是許多人研究的課題。但傳統方法的五點量表問卷只提供固定尺度的選擇，似乎無法完整地表達受測者真實且複雜的思考。因此本文將以模糊問卷調查進行試題難易度的探討。許多研究應用模糊平均數、模糊眾數或模糊中位數等概念於試題難易度評量。而本文將以此為基礎，定義一種新的距離，再透過一些轉換取得試題的難易度指標，進而比較各試題之間難度的差異。本文的另一個重點，是各個不同難度因子的向度來決定各試題的難度。再以模糊相對權重的概念，對各向度的難易度指標作加權，進而比較、分析。

　　Assessment for test difficulty have been the subject of many studies. The traditional method of a Likert scale questionnaire provides only a fixed scale choice, but it seems that we can’t fully express the real and complex thinking of respondents. Therefore, the thesis will apply fuzzy questionnaire to probe into test difficulty. Concepts such as Fuzzy mean, Fuzzy mode or Fuzzy median are applied in studies of assessment for test difficulty. The thesis will be based on these conceptions to define a new distance, and obtain the difficulty index of test through some conversion. Moreover, it will compare the differences of difficulty among test items. Another focus of this paper is to determine the difficulty of each item according to various dimensions of difficulty factors. Afterwards, the difficulty index of each dimension will be weighted, compared, and analyzed with the concept of fuzzy relative weight.

[1]王文俊(1997)。認識Fuzzy。台北：全華書局。
[2]江彥聖(2008)。模糊相關係數及其應用。國立政治大學應用數學系數學教
學碩士在職專班碩士學位論文。
[3]余民寧(2002)。教育測驗與評量－成就測驗與教學評量。台北：心理。
[4]阮亨中、吳柏林(2000)。模糊數學與統計應用。台北：俊傑。
[5]吳柏林(2005)。模糊統計導論：方法與應用。台北：五南。
[6]吳柏林(2002)。現代統計學。台北：前程。
[7]吳柏林(1997)。社會科學研究中的模糊邏輯與模糊統計分析。國立政治大
學研究通訊，7，17-38。
[8]波利亞(2006)。怎樣解題(蔡坤憲，譯)。台北：天下遠見。（原著第二版出版於1985年）
[9]黃新發、吳寶珍、連秀玉(2009)。應用模糊調查與統計分析國民中學基本
學力測驗。管理科學與統計決策，6(1)，50-62。
[10]Zadeh L.A. (1965) Fuzzy set. Information and Control,Vol. 8, 338-353.