直覺 c 模糊數聚類演算法

Intuitionistic fuzzy c-numbers clustering algorithm

沈亞承(YA CHENG SHEN)

指導教授 ： 楊敏生

中原大學/理學院/應用數學系/碩士(2022年)

https://doi.org/10.6840/cycu202201139

摘要

模糊c均值(Fuzzy c-means, FCM)聚類演算法是很常見的模糊聚類方法，主要的作用就是將給定的資料進行聚類的動作，此方法被提出後，又有許多延伸FCM的聚類演算法，目的都是優化聚類結果，我們利用Chaira(2011)提出的直覺模糊c均值(Intuitionistic FCM, IFCM)演算法，其特色就是加入游移度(hesitation degree)的概念，使聚類結果能夠更加理想，然而IFCM並不能有效地應用在模糊資料上，因此本論文將以IFCM作為基礎並擴展它，使其結合Yang & Ko (1996)提出的模糊c數(Fuzzy c-Numbers, FCN)聚類演算法，特此我們提出處理模糊資料的聚類演算法，稱之為直覺c模糊數(Intuitionistic FCN, IFCN)演算法，所提出的IFCN是透過模糊資料距離公式的改變所建立的聚類方法，IFCN不僅能夠保留原來IFCM的游移度特性，又能有效的應用在處理模糊資料上，我們將會比較IFCN演算法與FCN演算法，透過模擬資料和實際例子的聚類結果來比較IFCN和FCN之間的差異。

關鍵字

直覺模糊聚類 ； 模糊數 ； 模糊資料

並列摘要

Fuzzy c-means (FCM) clustering algorithm is a very common fuzzy clustering method. The main object is to cluster given data. After this method was proposed, there are many extensions to FCM. The purpose of clustering algorithms is to optimize the clustering results. We use the intuitionistic FCM (IFCM) algorithm proposed by Chaira (2011), which is characterized by adding the concept of hesitation degree. The clustering results based on IFCM can be better than FCM, but IFCM cannot be effectively applied to fuzzy data. In this paper, we shall take IFCM as the basis and then extend it by combining the fuzzy c-numbers (FCN) proposed by Yang & Ko (1996). Thus, we propose a clustering algorithm for processing fuzzy data, called Intuitionistic FCN (IFCN). The proposed IFCN is a clustering method that not only retain the original IFCM property, but also handle fuzzy data. By comparing IFCN with FCN with simulated data and actual examples, we present these different clustering results between IFCN and FCN.

並列關鍵字

Intuitionistic c-means ； Fuzzy data ； Fuzzy numbers

參考文獻

參考文獻

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[2] T. Chaira, "A novel intuitionistic fuzzy c means clustering algorithm and its application to medical images", Applied Soft Computing, Vol. 11, pp. 1711-1717, 2011.

[3] M.S. Yang and C.H. Ko, “On a class of fuzzy c-numbers clustering procedures for fuzzy data”, Fuzzy Sets and Systems, Vol. 84, pp. 49-60, 1996.

[4] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy set and on interval-valued fuzzy set, Fuzzy Sets and Systems, Vol. 78, pp. 305–316, 1996.