Presumably correct decision sets

The paper presents the presumably correct decision sets as a tool to analyze uncertainty in the form of inconsistency in decision systems. As a first step, problem instances are gathered into three regions containing weak members, borderline members, and strong members. This is accomplished by using the membership degrees of instances to their neighborhoods while neglecting their actual labels. As a second step, we derive the presumably correct and incorrect sets by contrasting the decision classes determined by a neighborhood function with the actual decision classes. We extract these sets from either the regions containing strong members or the whole universe, which defines the strict and relaxed versions of our theoretical formalism. These sets allow isolating the instances difficult to handle by machine learning algorithms as they are responsible for inconsistent patterns. The simulations using synthetic and real-world datasets illustrate the advantages of our model compared to rough sets, which is deemed a solid state-of-the-art approach to cope with inconsistency. In particular, it is shown that we can increase the accuracy of selected classifiers up to 36% by weighting the presumably correct and incorrect instances during the training process.