Three-way class-specific attribute reducts based on three-way weighted combination-entropies

Attribute reduction plays a fundamental role in data analysis, and it mainly resorts to algebraic and informational measures. Class-specific attribute reducts recently emerge for decision class optimization, and their algebraic type is initial while their informational types need developing. In this paper, three-way informational class-specific attribute reducts (including prior, posterior, and likelihood types) are established by introducing three-way weighted combination-entropies, which are hierarchically constructed for uncertainty measurement, and both their mutual relationships with algebraic class-specific reducts and their internal relationships with three-way informational systematicness are revealed. At first, three-way informational class-specific reducts are defined based on prior, posterior, and likelihood weighted combination-entropies, and their basic properties and heuristic algorithms are given. Then, optimization preservation conditions of three-way weighted combination-entropies are deeply mined to describe three-way informational reduction targets; thus, systematic relationships among informational and algebraic class-specific reducts are investigated, and relevant reduction strength and balance are acquired to generate derivation properties and algorithms of class-specific reducts. Finally, theoretical constructions and systematic connections of three-way class-specific reducts are validated via table examples and dataset experiments. This study deepens three-way uncertainty measurement and attribute reduction at the level of decision class, so it enriches three-way decision in terms of granular computing.