The Approaches Of Three-way Attribute Reduction Of Concept Lattices Based On Decision Formal Contexts

Formal Concept Analysis(FCA),also known as concept lattice theory,was founded in1982 by the German mathematician Wille.The basis of formal concept analysis is the formal context.The formal context can be expressed as a Boolean two-dimensional data table,where rows represent objects and columns represent attributes.According to the relationship between objects and attributes,a concept hierarchy can be established,which can be used for concept representation,concept ordering and conceptual reasoning.Formal concept analysis is an effective data analysis tool widely used in many fields.The attribute reduction of decision formal context is an important research content of formal concept analysis.The decision formal context form based on classical concept lattice has decision rule reduction,granular reduction,strong consistent reduction and so on.The three-way decision theory applied to the formal concept analysis,respectively proposed threeway concept lattices based on object and attribute-based derivation,and extended the research scope of formal concept analysis.This paper mainly studies the attribute reduction of threeway concept lattices based on objects in the decision formal context.The main research contents include:1.Proposed three-way decision rules and three-way necessary decision rules for the decision formal context.Defined three-way decision rule consistent set,and give Decision theorem of three-way decision rules consistent set.Combining the discernibility matrix and the discriminant function,gives three-way decision rule reduction methods.2.Based on the decision formal context,the concept of three-way granular consistent decision formal context and three-way granular consistent set are proposed to define the decision theorem of three-way granular consistent set is defined.The three-way granular reduction method is given by combining the discriminant matrix and the discriminant function.3.The relationship between three-way granular reduction,granular reduction and classification reduction is given.Combined with the equivalent description of the three-way decision rules,the relationship between three-way granular reduction,three-way strong consistent reductions,and three-way decision rule reduction is illustrated.