In　this　article,　assignment　reduction　and　approximation　reduction　are　proposed　for　Inconsistent　Ordered　Information　Systems　(IOIS).　The　properties　and　relationships　between　assignment　reduction　and　approximation　reduction　are　discussed.　The　dominance　matrix　and　decision　assignment　matrix　are　also　proposed　for　information　systems　based　on　dominance　relations.　The　algorithm　of　assignment　reduction　is　introduced,　from　which　we　can　provide　an　approach　to　knowledge　reductions　operated　in　inconsistent　systems　based　on　dominance　relations.　Finally,　an　example　illustrates　the　validity　of　the　given　method,　which　shows　that　the　method　is　effective　in　complicated　information　systems.　Copyright　©　2008,　Inderscience　Publishers.