Knowledge reduction in real decision formal contexts

Rule acquisition is one of the main purposes in the analysis of real decision formal contexts. In general, the decision rules derived directly from a real decision formal context are not concise or compact. In order to derive more compact decision rules, this study proposes a rule acquisition oriented framework of knowledge reduction for real decision formal contexts and formulates a corresponding reduction method by constructing a discernibility matrix and its associated Boolean function. The proposed reduction method is applicable to any real decision formal contexts and with the reduced real decision formal contexts, we can obtain more compact decision rules that can imply all the decision rules derived from the initial real decision formal context. Some numerical experiments are conducted to assess the efficiency of the proposed method.