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Dominance-based rough set approach is the extension of classical Pawlak rough set theories and methodologies, in which the information with preference-ordered relation on the domain of attribute value is fully considered. In the dominance-based information system, upper and lower approximations will be changed while the object set varies over time and the approximations need to be updated correspondingly for their variations result in changes of knowledge and rules. Considering that three-way decisions is a special class of general and effective human ways of problem solving and information processing, a new incremental maintenance mechanism using three-way decisions is proposed in this paper, namely, the universe is divided into three pair-wise disjoint subsets firstly, then appropriate strategies are developed and acted on each subsets. Furthermore, the corresponding methods for updating the approximations of upward unions and downward unions of decision classes are analyzed systematically under the variations of object set in the dominance-based information system from the perspective of three-way decisions. Moreover, considering vector representation and calculation is intuitive and concise, two incremental update algorithms of approximations are suggested and implemented in the MATLAB platform. Finally, some tests on data sets from UCI (UC Irvine Machine Learning Repository) are undertaken to verify the effectiveness of the proposed methods. Compared with the non-incremental updating methods, the proposed incremental updating method with three-way decisions generally exhibits a better performance.

Dynamic Knowledge Update Using Three-Way Decisions in Dominance-Based Rough Sets Approach While the Object Set Varies