Abstract: In inconsistent decision systems,attribute reduction models are non-equivalent between algebra view and information view.Skowron's discernibility matrix provides a kind of normative and precise mathematical model for finding attribute reduction under algebra view.However,this discernibility matrix can't describe the attribute reduction characteristic of an inconsistent decision system under information view.This paper defines simplified decision system based on the decision distribution function of condition equivalence class,and designs the discernibility matrix satisfying algebra view and information view.The Reasoning proof and simulation example shows the feasibility and effectiveness of the proposed method.