Incrementally updating approximations based on the graded tolerance relation in incomplete information tables

The incremental learning methods based on rough set theory are effective in acquiring knowledge in dynamically changing information tables. In this paper, we focus on the effective acquisition of decision rules by incrementally updating approximations when an incomplete information table changes. First of all, we present a four-step model to obtain three-way decision rules in an incomplete information table based on the graded tolerance relation. The first step presents the graded tolerance relation between objects. The second step calculates the degrees of objects belonging to approximations by using fuzzy logic operators. Besides, we propose a relation matrix to calculate the degrees efficiently. The third step gets three-way approximations by applying a pair of thresholds to the degrees. The fourth step obtains three-way decision rules based on the descriptions of objects. According to the four-step model, we find the notion of approximations plays an essential role in rule acquisition. Incrementally updating approximations are an effective method to obtain decision rules when an incomplete information changes. Accordingly, we study the incrementally updating approximations by incrementally updating the relation matrix when changing attributes, objects, and the attribute value of an object. Finally, experimental results illustrate that the incremental methods are more effective than non-incremental methods.