Abstract: Formal concept analysis was proposed by Wille R.in 1982.It is a model for the study of formal concepts and conceptual hierarchies.As an effective tool in knowledge discovery,it has been applied in various research areas such as information retrieval,data mining and pattern recognition.In practical applications,there may be a lot of redundant attributes in the formal context.Therefore,it is necessary to study the attribute reduction in formal concept analysis,and finding more concise approaches of attribute reduction is an important aspect in formal contexts.In this paper,inspired by the idea of rough set theory,attribute reduction in inconsistent decision formal contexts was studied.Some scholars proposed four definitions of distribution reduction,maximum distribution reduction,assignment reduction,and approximation reduction based on equivalency class in inconsistent information systems.As a formal context is a special information system,in this paper,substituting the equivalency class by the granular set,four new definitions of distribution reduction,maximum distribution reduction,assignment reduction,and upper approximation reduction based on inclusion degree were proposed.It is proved that the distribution reduction must be the maximum distribution reduction,the distribution reduction must be the assignment reduction,and the assignment reduction is equivalent to the upper approximation reduction.As an example,the judgement theorem for assignment consistent set was proved,and Boolean method for assignment reduction were given.

Key words: Attribute reduction, Consistent set, Decision formal contexts, Discernibility matrix