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Clustering techniques are used to split data into clusters where each cluster contains elements that look more similar to elements in the same cluster than elements in other clusters. Some of these techniques are capable of handling clustering process uncertainty, while other techniques may have stability issues. In this paper, a novel method, called Minimum Information Gain Roughness (MIGR), is proposed to select the clustering attribute based on information entropy with rough set theory. To evaluate its performance, three benchmark UCI datasets are chosen to be clustered by using MIGR. Then, the resulting clusters are compared to those which are resulted from applying Min-Min-Rough (MMR) and information-theoretic dependency roughness (ITDR) algorithms. Both last-mentioned techniques were already compared with a variety of clustering algorithms like k-modes, fuzzy centroids, and fuzzy k-modes. The Global purity, the overall purity, and F-measure are considered here as performance measures to compare the quality of the resulting clusters. The experimental results show that the MIGR algorithm outperforms both MMR and ITDR algorithms for clustering categorical data. [ABSTRACT FROM AUTHOR]