One　of　the　focuses　of　rough　set　theory　is　attribute　reduction.　In　an　ordered　information　system,　the　information　quality　and　significance　of　attributes　are　defined.　Relationships　between　them　and　attribute　reductions　are　investigated,　based　on　which,　a　heuristic　algorithm　for　obtain　attribute　reductions　is　presented,　and　the　time　complexity　of　the　algorithm　is　also　shown.　Finally,　the　validity　of　the　algorithm　have　been　depicted　by　an　practical　example.