“…In the clustering attribute selection based on rough cluster analysis, the attribute is selected to split according to the roughness of the attribute or the attribute dependencies, e.g., Min-Min Roughness (MMR) [43], Maximum Dependency of Attribute (MDA) [44], Maximum Attribute Relative (MAR) [45], and Mean of Accuracy of approximation using variable precision of attributes (MA) [46], all of which are related to approximations computation. In rough set based cluster ensemble method [47,48,49], the computation of approximations is a necessary step. Hence, it is meaningful and valuable to develop an efficient algorithm for computing approximations, which can accelerate the data mining or machining learning related tasks under a dynamic environment, e.g., attribute reduction, rule induction, cluster analysis and cluster ensemble.…”