A variety of cluster analysis techniques prerequisite to cluster objects having similar characteristics in data mining. But the clustering of those algorithms have lots of difficulties in dealing with categorical data within the databases. The imprecise handling of uncertainty within categorical data in the clustering process stems from the only algebraic logic of rough set, resulting in the degradation of stability and effectiveness. This paper proposes a information-theoretic rough entropy(RE) by taking into account the dependency of attributes and proposes a technique called min-mean-mean roughness(MMMR) for selecting clustering attribute. We analyze and compare the performance of the proposed technique with K-means, fuzzy techniques and other standard deviation roughness methods based on ZOO dataset. The results verify the better performance of the proposed approach.