Enhanced rough–fuzzy c-means algorithm with strict rough sets properties

Abstract

In real applications, it may be impossible to obtain complete information of a given pattern set. Uncertain information will cause imperfect description for a pattern set in various pattern recognition algorithms. It is natural to expend great effort on analyzing the belonging of patterns with large uncertainties. Fuzzy sets theories are reputed to handle vague phenomena through membership functions which measure degrees of a pattern belonging to different clusters. Rough sets theory is a new paradigm to deal with uncertainty and incompleteness, forming an interesting region which consisted of patterns with large uncertainties. By integrating fuzzy sets and rough sets, a hybrid unsupervised learning algorithm is designed for analyzing patterns with large uncertainties. Furthermore, a fuzzy weighted factor is designed to work with membership degrees together for further determining where patterns with large uncertainties belong to. Besides, the partition criterion utilized in original hybrid clustering algorithms cannot guarantee basic rough sets properties to be fully satisfied. In this study, a modified partition criterion is proposed to overcome this issue. Experimental results on synthetic datasets, real-life datasets, and image segmentation problems indicate that the proposed method outperforms its counterparts in most cases.