One focus of data analysis in formal concept analysis is attribute-significance measure, and another is attribute reduction. From the perspective of information granules, we propose information entropy in formal contexts and conditional information entropy in formal decision contexts, and they are further used to measure attribute significance. Moreover, an approach is presented to measure the consistency of a formal decision context in preparation for calculating reducts. Finally, heuristic ideas are integrated with reduction technique to achieve the task of calculating reducts of an inconsistent data set.