Type-II Fuzzy Possibilistic C-Mean Clustering

Abstract

Fuzzy clustering is well known as a robust and efficient way to reduce computation cost to obtain the better results. In the literature, many robust fuzzy clustering models have been presented such as Fuzzy C-Mean (FCM) and Possibilistic C-Mean (PCM), where these methods are Type-I Fuzzy clustering. Type-II Fuzzy sets, on the other hand, can provide better performance than Type-I Fuzzy sets, especially when many uncertainties are presented in real data. The focus of this paper is to design a new Type-II Fuzzy clustering method based on Krishnapuram and Keller PCM. The proposed method is capable to cluster Type-II fuzzy data and can obtain the better number of clusters (c) and degree of fuzziness (m) by using Type-II Kwon validity index. In the proposed method, two kind of distance measurements, Euclidean and Mahalanobis are examined. The results show that the proposed model, which uses Mahalanobis distance based on Gustafson and Kessel approach is more accurate and can efficiently handle uncertainties.