Three-way class-specific attribute reducts from the information viewpoint

By virtue of granular computing, attribute reduction of rough sets can effectively perform information processing. Regarding the decision table with granular structures, the traditional classification-based attribute reducts at the macro-top already have the algebra and information interpretations, while the new class-specific attribute reducts at the meso-middle currently have only the algebra explanation. Aiming at the class-specific reducts, this paper establishes three-way types from the information viewpoint, and it further compares the information and algebra types. At first, the three-way information class-specific reducts (including the likelihood, prior, and posterior types) are systematically proposed by using the three-way weighted entropies with uncertainty measurement. Then, optimization preservation conditions of the positive region and weighted entropy are deeply mined to describe reduction targets of the algebra and information types, and relevant conditions related to knowledge coarsening are effectively represented by the granular merging and three-way regions. Furthermore, all four types of class-specific reducts gain their relationships, including the strong-weak relationship based on optimization preservation conditions, the degeneration relationship based on consistency and inconsistency, and the information relationship based on systematic equalities. Finally, algebra and information class-specific reducts and their relationships are verified by a consistency example and an inconsistency example. As a conclusion, the four types of class-specific reducts adopt distinctive algebra or information perspectives to present the difference and emphasis, especially in the inconsistency case, and they have in-depth mutual relationships. This study provides novel insight into attribute reduction based on granular computing, mainly via the information theory and three-way decisions. (C) 2018 Elsevier Inc. All rights reserved.