基於粗糙集合理論具決策試題之試題擴增動態約簡演算法

Item Dynamic Incremental Reduction Algorithm of Item Response System with Decision Item Based on Rough Set Theory

周世忠(Chou Shih-chung)

指導教授 ： 劉湘川

亞洲大學/資訊學院/資訊工程學系碩士在職專班/碩士(2011年)

摘要

粗糙集合理論是一種處理含糊性和不確定性問題的數學新工具。相較於其他傳統理論，粗糙集合理論不需要準備任何數據或是額外的資訊假設。劉湘川(2008)首先提出基於粗糙理論之試題作答反應系統，可應用於小班教學測驗之試題題庫約簡。而劉湘川、簡茂發、許天維、周世忠(2010)發表之「試題反應系統具決策試題之擴增動態約簡演算法」屬性約簡理論，更進一步提出兼具條件屬性與決策屬性之屬性擴增動態約簡演算法，經轉化應用於試題作答反應系統。 本研究將以程式語言 MATLAB 撰寫程式，運用「試題反應系統具決策試題之擴增動態約簡演算法」將條件試題判別矩陣擴增為兼顧條件試題與決策試題之共同判別矩陣，同時將動態增加之條件試題在先期滿足決策試題之約束條件下適當地分類。本研究的成果如下： 1. 設計「具決策試題之試題擴增動態約簡演算法」應用程式。 2. 藉上述應用程式定義擴增的試題並判斷是否為必要試題，以利教師進行補救教學。 3. 方便建立小班級教學測驗之複本試題題庫或精要之試題題庫。

關鍵字

粗糙集合理論 ； 試題作答反應系統 ； 試題約簡 ； 條件試題 ； 決策試題

並列摘要

Rough Set Theory is a new mathematical tool which deals with vagueness and uncertainty. Compared with other traditional theories, rough set theory does not need any data or extra informational hypotheses. In 2008, Liu Xiang-chuan first indicated that Item Response System based on Rough Set Theory can be applied to item reduction of test in a small class. The attribute reduction theory based on Item Dynamic Incremental Reduction Algorithm of Item Response System issued by Liu Xiang-chuan, Jian Mao-fa, Xu Tian-wei and Chou Shih-chung in 2010 went further to proposed that Attribute Incremental Dynamic Reduction Algorithm which combines conditional attribute and decisional attribute can be transformed and applied to Item Response System.
This research has used Matlab language to write a program and employs Item Dynamic Incremental Reduction Algorithm of Item Response System with Decisional Item to amplify conditional item discriminating matrix into common discriminating matrix, which can take into consideration both conditional items and decisional items and at the same time adequately classifies the dynamically increased conditional items only when they qualify as decisional items.

The results are stated as follows:
1. Design the application program of ‘Item Dynamic Incremental Reduction Algorithm of Item Response System with Decisional Item’.
2. Help the teachers preceding the retrieval teaching by using the program above to define the incremented items and judge them as necessary or not.
3. Help to establish the bank of duplicated or fundamental items used in tests in a small class.

並列關鍵字

Rough Set Theory ； Item Response System ； item reduction ； conditional item ； decisional item

參考文獻

劉湘川、郭昭麟、陳家蓁 (2009) 。基於粗糙理論之試題擴增動態約簡演算法。2009 年中國測驗學會年會暨學術研討會。10月24日。台北市，國立臺灣師範大學。

Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data. London.

一、中文部分

李雄飛、李軍 (2003) 。數據挖掘與知識發現。高等教育出版。

温坤禮、永井正武、張廷政、温惠筑(2008)。粗糙集入門及應用。五南圖書出版。