Aiming　at　the　dynamic,　uncertain　feature　and　hazardness　of　public　emergency,　the　concepts　of　the　hazard　affected　class,　F--hazard　affected　quantity,　F--hazard　affected　loss,　F--hazard　affected　degree,　F--hazard　affected　loss　law　and　F--hazard　affected　degree　law　are　presented　by　using　dual　of　one-directional　singular　rough　sets.　Using　the　presented　concepts,　the　relation　theorems　between　F--hazard　affected　loss　and　F--hazard　affected　degree,　F--hazard　affected　loss　law　and　F--hazard　affected　law　are　proposed.　At　last　the　discrimination　theorem　of　F--risk　attribution　intrusion　law,　and　the　recognition　rule　of　F--hazard　affected　degree　law　and　its　application　are　also　given.　One-directional　singular　rough　sets　are　a　new　and　useful　mathematics　tool　in　the　study　of　the　emergency　management　theory　and　method.