Rough-Fuzzy Clustering Based on Two-Stage Three-Way Approximations

A general framework of rough-fuzzy clustering based on two-stage three-way approximations is presented in this paper. The proposed framework can deal with the uncertainties caused by the membership degree distributions of patterns. In the first stage (macro aspect), three-way approximations with respect to a fixed cluster can be formed from the global observation on data which can capture the data topology well about this cluster. In the second stage (micro aspect), the fuzziness of individual patterns over all clusters can be measured with De Luca and Termini's method, based on which three-way approximations with respect to the whole data set can be generated such that the uncertainties of the locations of individual patterns can be detected. By integrating the approximation region partitions obtained in the two stages, i.e., using the partition results obtained in the second stage to modify the partition results obtained in the first stage, the misled prototype calculations can be verified and the obtained prototypes tend to their natural positions. Comparative experiments on a synthetic data set and some benchmark data sets demonstrate the improved performance of the proposed method.