The　maximizing　set　and　minimizing　set　method　is　a　popular　ranking　approach　for　fuzzy　numbers,　which　ranks　them　based　on　their　left,　right　and　total　utilities.　This　paper　presents　an　alternative　ranking　approach　for　fuzzy　numbers　called　area　ranking　based　on　positive　and　negative　ideal　points,　which　defines　two　new　alternative　indices　for　the　purpose　of　ranking.　The　two　new　indices　are　defined　in　terms　of　a　decision　maker　(DM)＇s　attitude　towards　risks　and　the　left　and　the　right　areas　between　fuzzy　numbers　and　the　two　ideal　points.　It　is　shown　that　the　area　ranking　approach　has　strong　discrimination　power　and　can　rank　fuzzy　numbers　that　are　unable　to　be　discriminated　by　the　maximizing　set　and　minimizing　set　method.　It　is　also　shown　that　the　DM＇s　attitude　towards　risks　may　have　a　significant　impact　on　the　ranking　of　fuzzy　numbers.　As　a　side　product,　a　new　defuzzification　formula　is　also　developed　and　discussed.　©　2009　Elsevier　Ltd.　All　rights　reserved.