In inconsistent decision systems

attribute reduction models are non-equivalent between algebra view and information view.Skowrons discernibility matrix provides a kind of normative and precise mathematical model for finding attribute reduction under algebra view.However

this discernibility matrix cant 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.