In this paper, we propose a new measure based on the confidence of Bayesian posterior probability so as to reduce unimportant information in the clustering process. Because the performance of clustering is up to selecting the important degree of attributes within the databases, the concept of information entropy is added to posterior probability for attributes discernibility. Hence, The same value of attributes in the confidence of the proposed measure is considerably much less due to the natural logarithm. Therefore posterior probability-based clustering algorithm selects the minimum of attribute reducts and improves the efficiency of clustering. Analysis of the validation of the proposed algorithms compared with others shows their discernibility as well as ability of clustering to handle uncertainty with ACME categorical data.