Abstract: Formal concept analysis is a theory of data analysis using concept lattice,and attribute reduction is one of the main ways of concept lattice reduction.Decision implication is a knowledge representation and reasoning model of formal concept analysis in decision situations.In the existing research on attribute reduction that preserves decision context knowledge information,concept rules or granular rules are usually used to preserve decision context knowledge information.Compared with concept rules and granular rules,decision implication has a stronger ability of knowledge representation.To further reduce the difference between the representation of knowledge information before and after attribute reduction,a study is conducted on attribute reduction which preserves decision implication.Firstly,based on the semantics of decision implication,the definitions of consistent set and reduction that preserve decision implication aregiven,and the necessary and sufficient conditions for determining consistent set and reduction are provided.Examples show the problems of the reduction,and by combining implication theory,the definitions of weak consistent set and weak reduction are introduced.Then,the rationality of weak reduction compared with reduction is analyzed from the perspective of knowledge inclusion.Finally,the necessary and sufficient conditions for judging weak consistent set and weak reduction are provided,and the method that can find weak reduction is given by combining decision implication canonical basis,which enriches the research of attribute reduction that preserves knowledge information.

Key words: Formal concept analysis, Attribute reduction, Decision implication, Knowledge representation model, Decision implication canonical basis