對於一個有效的辨識系統，擁有線上學習的特性是十分重要的，線上學習能夠快速學習新的事物及微調原有資訊，但又無損於舊的資訊。近年來，有許多線上學習系統被提出來，模糊適應共振理論映射圖(Fuzzy Adaptive Resonance Theory Map，簡稱Fuzzy ARTMAP)即為其中最著名的線上學習系統之一，雖然有許多引人的特性，Fuzzy ARTMAP系統一直面臨著計算負荷過重及架構冗雜的問題，因此本論文提出一種新的以簡化Fuzzy ARTMAP系統為基礎之線上學習系統，該系統可應用於圖樣識別與函數逼近的問題。本論文所提出的線上學習系統效能，不僅只以一些人工資料集來評估，也以稅務資料集來測試其效能。我國稅務稽徵機關之營利事業所得稅一向採用選案查核方式來查緝逃漏稅，由於審查人力及資源的有限，查核結果往往成效不彰，本線上學習系統可被訓練用於提升逃漏稅查核結果，其研究目的為：(1)達到可接受的正確預測結果、(2)防止審查人力的工作負荷過重及(3)杜絕逃漏稅之投機現象。 For an efficient pattern recognition system, it is important to possess the property of the on-line learning. The on-line learning property is referred to the ability of learning new classes and refining existing classes quickly and without destroying old class information. Recently, many on-line learning systems have been proposed. One of the most famous on-line learning systems is the Fuzzy Adaptive Resonance Theory Map (Fuzzy ARTMAP). Despite many appealing properties, the Fuzzy ARTMAP system suffers from the computation overhead and architectural redundancy. In this paper, a new on-line learning system based on the simplified Fuzzy ARTMAP is proposed. The proposed system can be applied in pattern recognition and function approximation problems. The performance of the proposed on-line learning system is evaluated by not only some artificial data sets but also the tax data set. The only way employed by Taiwan tax office to investigate business income tax evasion is to reexamine some randomly selected case. Owing to limited human resources, the performance of the investigation is usually not effective and efficient. In this thesis, the proposed on-line learning system was trained to improve the performance of investigating tax evasion. Targets of this research are (1) to achieve an acceptable degree of accurate prediction, (2) to prevent inspectors from overloading, and (3) to stop the speculative phenomenon of tax evasion.