Centroid　defuzzification　and　the　maximizing　set　and　minimizing　set　methods　are　two　commonly　used　approaches　to　ranking　fuzzy　numbers　and　often　require　membership　functions　to　be　known.　In　this　paper,　the　two　methods　are　reinvestigated　when　explicit　membership　functions　are　not　known　but　alpha　level　sets　are　available.　Two　analytical　formulas　are　derived　under　the　assumption　that　the　exact　membership　functions　can　be　approximated　by　using　piecewise　linear　functions　based　on　alpha　level　sets.　The　derived　analytical　formulas　are　of　significant　importance　and　provide　very　useful　decision　supports　for　a　wide　variety　of　applications　of　the　two　methods　in　industrial　engineering　and　other　areas.　Numerical　examples　are　offered　to　test　the　derived　formulas　and　illustrate　their　computational　processes　and　applications　in　risk　assessment　of　a　software　development.　©　2008　Elsevier　Ltd.　All　rights　reserved.