摘要
在聚類分析的領域中，許多新的方法被提出，但它們大多是應用於實數值資料，然而在真實情況中也會出現一些無法明確定義清楚的資料，如同模糊型資料等。於模糊C均值(Fuzzy C-Means,FCM)被提出後，延伸出了許多有著不同特色的新聚類方法，其中Guo在2015年時將FCM進行延伸並提出了新的中位C均值(Neutrosophic C-Means,NCM)聚類方法，此方法針對FCM容易受噪音點影響的缺點進行改善，有效降低了噪音點對聚類結果的影響。為了解決模糊型資料(Fuzzy Numbers)的聚類問題，Ko與Yang在1996年延伸了FCM至模糊型資料上，使其能夠處理模糊資料，並稱其為模糊C數(Fuzzy C-Numbers,FCN)聚類法。在本篇論文中，我們將結合NCM與FCN延伸出一種新的聚類方法，其包含了NCM所具備的降低噪音點影響的特色，並能夠處理模糊型資料，我們將其稱為中位C模糊數(Neutrosophic C-Numbers,NCN)聚類演算法。為了觀察此方法是個好的方法，我們對其以一些模擬資料與實際資料進行測試，並將結果與其他處理模糊資料的聚類方法進行比較，而結果顯示了此方法在有噪音點的情況下確實是一個較好的方法。
並列摘要
In the field of cluster analysis, many new methods have been proposed, but most of them are applied to real-valued data. However, in real situations, there are some data that can be only defined with vagueness, such as fuzzy data. After Fuzzy C-Means (FCM) was proposed, many new clustering methods with different characteristics were extended. Among them, Guo extended FCM in 2015 and proposed a new Neutrosophic C-Means (NCM) clustering method. This method improves the disadvantage that FCM is easily affected by noise points, and effectively reduces the influence of noise points on the clustering results. To solve the clustering problem of fuzzy data, Ko and Yang in 1996 extended FCM for handling fuzzy numbers, so that it can deal with fuzzy data, and called Fuzzy C-Numbers (FCN). In this thesis, we will combine NCM and FCN to propose a new clustering method, which includes the features of NCM to reduce the influence of noise points, and can be also applied to fuzzy data. We call it Neutrosophic C-Numbers (NCN) clustering algorithm. To see if this method is a good one, we test it on some simulated data and real data. By comparing the results of the proposed NCN with other clustering methods, we find that the proposed method works better, especially under the case of noise points.