Core set analysis in inconsistent decision tables

Core set inconsistency always causes confusion regarding how to select the proper core set for data reduction in inconsistent decision tables. In this paper, partitions of knowledge granules are introduced to analyze this inconsistency, and it is concluded that there are only three types of effective partitions: those that focus on exact information, those that focus on exact, partial, and negative information and those that focus on exact, partial, negative, and probabilistic information. All useful core sets are calculated systematically by converting the three types of partitions to corresponding discernibility matrices. Then, we define three types of rules, positive, inexact, and confidence rules, based on the three types of partitions. Using these rules, an intelligible rule-based strategy is proposed to select the proper core set for a practical application, which resolves the confusion caused by core set inconsistency and completes the process of data reduction. Experimental analysis and industrial results demonstrate the effectiveness of the selection strategy.