模糊口語評估尺度之歸屬函數建構及特性探討

Fuzzy Membership Functions of Verbal Evaluation Terms

林信惠(Hsin-Hui Lin) ； 蕭文峰(Wen-Fung Shaw)

《資訊管理學報》 8卷1期 (2001/07) Pp. 1-19

https://doi.org/10.6382/JIM.200107.0001

摘要

Thurstone主張個體的意見可由三個不同指標描述：意見的全距(range)、均值(mean)、代表點(representiveness)。由於傳統數學並沒有適當的方法用以處理區間(interval)與非對稱性的運算，因此雖然這些觀點早已被提出，但後續方法卻沒能成功地擷取這些複雜性。模糊理論的出現提供意見表達與運算的新契機“然而，以往歸屬函數的建構方法採用點估計的方式來獲取，其限制在於只能獲取「感覺屬性」型態的歸屬函數。本研究提議以區間方式來獲取「心理屬性」型態的歸屬函數。所提方法可同時建構五等級口語評估值之歸屬函數。由Cronbach（計算得知本方法達相當高的信度(0.88）。
由觀察所建構的歸屬函數顯示：人類的偏好當轉成模糊評估尺度時，與等權重、等間隔的數值評估（即等距尺度）或對稱的簡化型歸屬函數是不一致的。另外，歸屬函數之分佈圖形亦顯示模糊理論中的「正規化」及「修飾詞」運算是不恰當的。最後，由比較實證型與簡化型的歸屬函數在綜合模糊口語評估詞上的差異發現：實證型歸屬函數在以模糊數(fuzzy number)進行運算時與簡化型歸屬函數有顯著的差異。這些結果可供社會科學研究者引入模糊集合理論的參考。

關鍵字

模糊口語評估 ； 歸屬函數建構 ； 實驗法 ； 模擬 ； 心理屬性

並列摘要

Thurstone argues that an individual's opinion could be characterized in terms of three different indexes: the range of the opinion, the mean of the opinion, and the best representative point of the opinion. Due that traditional mathematics was not well developed for dealing with ranges and asymmetries, though these insights were identified early in the development of attitude measurement, the subsequent methods failed to capture this complexity. The inception of fuzzy sets theory brings new methods for representing and manipulating opinions. However, the traditional point estimation methods for constructing membership functions are subject to modality attributes. This study proposes an interval estimation method to construct the membership functions for mental attributes. The proposed method can simultaneously construct five categories of verbal evaluation terms. The Cronbach α, 0.88, shows that the method is quite reliable.
By observing the constructed membership functions, we learn that the human preference is not consistent with equal-weighted, equal-spaced numerical evaluations. Nor is it consistent with simplified, symmetric triangular or trapezoidal membership functions. Furthermore, the essential questions about the operations regarding to ”normalization” and ”modifier” are also discussed. We conduct a computer simulation to understand the difference between the constructed membership functions and the simplified membership functions. The results show that empirical membership functions and simplified membership functions have significant differences, especially when they are manipulated by fuzzy number operators. These results may benefit social scientist in applying fuzzy sets theory.

並列關鍵字

Fuzzy verbal evaluations ； Membership function construction ； Experiment ； Simulation ； Psychological attribute

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