電腦化適性測驗依照受試者的能力，試圖提供最適合受試者作答的試題，達到最佳的測驗效果。雖然Maximum Likelihood Estimation (MLE)及Bayesian Likelihood Estimation (BLE)被提出用以解決能力評估且有不錯的效果，但是並未考慮受試者作答值與其能力不符合和能力評估標準差異動的情形。我們認為使用調適性網路模糊推論系統(ANFIS)藉由收集受試者在能力評估的相關資料，自動推論出具彈性化的能力評估值，可以有效改善評估成效。因此，本研究提出以ANFIS為基礎的學習能力新預測模型，並以試題反應理論為依據，適性化選擇試題。利用電腦化適性測驗中試題的鑑別度、困難度、猜測度及受試者作答試題前的能力作為參數，使用ANFIS推論受試者的能力修正量，評估受試者作答後的能力。實驗係以MATLAB軟體建構ANFIS模式，模擬受試者作答以收集三種不同評估情形下之訓練資料，透過各種不同的ANFIS模糊規則組合情形來推論能力提升量，以提升評估能力的準確度，其推論能力值與真實能力值之間的誤差值並與MLE及BLE兩種方法比較。實驗結果顯示，在試題訊息量較大時，ANFIS評估能力誤差值較小，可提供較好的能力評估準確度，進而提供更符合受試者能力的試題。
關鍵詞：ANFIS、試題反應理論、電腦化適性測驗

Computerized adaptive testing attempts to provide the most suitable question for an examinee depending on the examinee’s ability to achieve the best result. Although Maximum Likelihood Estimation (MLE) and Bayesian Likelihood Estimation (BLE) have been provided to solve ability estimation and have good results in the literature, little attention has been paid to the situation when the answer of an item does not conform with the examinee’s ability as expected nor standard derivation changes of the ability estimation. We hypothesized that the Adaptive-Network-Based Fuzzy Inference System (ANFIS) can be used to infer flexible examinee’s ability estimation automically by analyzing the relevant data of the examinee in a test. Consequently, the study presents a novel learning ability model based on ANFIS, which can adaptively choose questions by Item Response Theory. Taking the item discrimination, difficulty, guessing, and the examinee’s ability before he/she answers a question as parameters, the proposed method can infer the adjustment of the examinee’s ability to update its value after he/she answers the question. The ANFIS model of the experiments were developed using MATLAB. The examinees were simulated and the training data were collected under three different situations. Through different combination of ANFIS fuzzy rules, the adjustment of ability is inferred to improve the accuracy of the estimated ability. The error between the true ability and the estimated ability obtained by the proposed model is compared with MLE and BLE. The simulation results show that the estimated ability error of ANFIS is smaller than MLE and BLE when the value of the test information is larger. The proposed method could provide better accuracy of the examinee’s ability and offer more appropriate questions for examinees.
Keywords: ANFIS, Item Response Theory, Computerized Adaptive Testing

Chapter 1 Introduction 1
Chapter 2 Literature Reviews 4
Chapter 3 Background Concepts 9
3.1 Adaptive-Network-Based Fuzzy Inference System (ANFIS) 9
3.1.1 Fuzzy Set Theory 9
3.1.2 Fuzzy Inference System 10
3.1.3 Structure of ANFIS 12
3.2 Item Response Theory (IRT) 17
3.2.1 Classic Test Theory and Item Response Theory 17
3.2.2 IRT Assumption 20
3.2.3 Ability Estimation of Examinees 25
3.3 Item Information Function 27
Chapter 4 Ability Estimation of Students by ANFIS 30
4.1 The Simulation of Producing Data Set 30
4.2 The Inference of Ability Adjustment Using ANFIS 36
4.3 Ability Estimation by ANFIS 40
Chapter 5 Simlation Results 45
Chapter 6 Conclusion 72
References 75

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