In　this　paper,　concepts　of　knowledge　entropy　and　knowledge　entropy-based　uncertainty　measures　are　given　in　incomplete　information　systems　and　decision　systems,　and　some　important　properties　of　them　are　investigated.　From　these　properties,　it　can　be　shown　that　these　measures　provide　important　approaches　to　measure　the　uncertainty　ability　of　different　knowledge　in　incomplete　decision　systems.　Then　the　relationships　among　these　knowledge　entropies　proposed　are　discussed　as　well.　A　new　definition　of　reduct　is　proposed　and　a　heuristic　algorithm　with　low　computational　complexity　is　constructed　to　improve　computational　efficiency　of　feature　selection　in　incomplete　decision　systems.　Experimental　results　demonstrate　that　our　algorithm　can　provide　an　efficient　solution　to　find　a　minimal　subset　of　the　features　from　incomplete　data　sets.