二型模糊C均值聚类算法及其应用

摘要

提出一种简化的、带有确认程度的隶属度的二型模糊集,利用其设计二型FCM聚类算法,推导出其迭代求解公式.研究发现,二型FCM算法的目标函数和迭代求解公式是原有FCM算法的推广,数学表达简洁.在人工数据集和黄瓜数据集上的应用表明,该算法可以通过确认程度的影响,得到更加精确的FCM算法聚类中心的位置,可有效甄别出异常点,说明算法的有效性.%A simplified type-2 fuzzy set with confirmation degree is proposed,base on which a new type-2 fuzzy C-means (FCM) algorithm is designed,and its iterative solution is given.It is easy to see that the objective function and iterative solution have concise mathematical form,and are the generalization of the results of traditional FCM.Experimental results on an artificial dataset and a cucumber leave dataset show that type-2 FCM is effective in finding cluster centers and membership degrees.Compared with FCM,type-2 FCM can find a more precise cluster center,and the outliers can be detected by the role of confirmation degrees.