Updating three-way decisions in incomplete multi-scale information systems.

Three-way decisions theory has been developed and applied to decision making in uncertain environments. Decision tasks under ambiguity involving both missing values and hierarchical concept are abundant in real-world applications. In this paper, we study the update problem of three-way decisions with dynamic variation of scales in incomplete multi-scale information systems. The updating mechanisms of decision granules induced by the similarity relation are exploited with the cut refinement and coarsening through the attribute value taxonomies, and the dynamic tendencies of conditional probability are hence estimated with evolving granularity structure. Reasonable updating behaviors of probabilistic parameters are characterized in the framework of decision-theoretic rough sets, in order to relate optimism and pessimism decision making on the basis of the variation in attitudes to losses or costs of decisions during the periodic transformation between coarser granular-scale and refiner granular-scale of data. Then the dynamic tendencies of conditional probability with the updating behaviors of probabilistic parameters together are incorporated into the incremental process of updating three-way decisions. Theoretical justifications and semantic interpretations are provided to guarantee the satisfaction of the proposed method for incremental three-way decisions in multi-scale incomplete information systems. Experimental results on several UCI datasets show that the proposed incremental algorithms efficiently update three-way decisions for handling transformation of data scales caused by the cut refinement and coarsening through the attribute value taxonomies.