A unified framework of dynamic three-way probabilistic rough sets.

The incremental learning technology has been widely applied in efficient and effective data mining with big data based on granular computing, rough sets and three-way approaches. In real-life applications, the information systems will evolve over time with four levels of variational situations, which can be described by the combination of the variations of attributes, objects, condition attributes values and decision attributes values. Considering updating knowledge with multilevel variations of data, this paper proposes a unified dynamic framework of decision-theoretic rough sets for incrementally updating three-way probabilistic regions, namely, positive region, boundary region and negative region. Through improving the representation of three-way regions based on the well-established Bayesian decision procedure, a novel matrix approach is introduced by the construction of Boolean matrix and specific definition of matrix operation. Subsequently, at the variations of level-1, the fundamental updating propositions, which can induce the corresponding propositions with the variations of level-2, level-3, level-4, respectively, are presented by the matrix updating strategies. Finally, experiments with four incremental algorithms developed for the verification of feasibility and efficiency under multilevel variations of data are conducted by comparison with non-incremental algorithm.