This paper extends the concept reduction in formal context to formal decision context, and studies the concept reduction preserving antecedent information of rules in weakly consistent formal decision context. Firstly, the conditional subcontext is compressed to form the antecedent context by only considering the binary relation in the antecedent of the rules of formal decision context. Then, we propose the concept reduction preserving antecedent information of rules for the antecedent context, and give the judgment theorem of concept consistent set by representative concept matrix. Finally, we classify all formal concepts into three parts according to the role of each formal concept in concept reduction, and discuss the concept characteristics of three types of formal concepts from the perspective of the minimal representative concept matrix.