Failure　mode　and　effects　analysis　(FMEA)　has　been　extensively　used　for　examining　potential　failures　in　products,　processes,　designs　and　services.　An　important　issue　of　FMEA　is　the　determination　of　risk　priorities　of　the　failure　modes　that　have　been　identified.　The　traditional　FMEA　determines　the　risk　priorities　of　failure　modes　using　the　so-called　risk　priority　numbers　(RPNs),　which　require　the　risk　factors　like　the　occurrence　(O),　severity　(S)　and　detection　(D)　of　each　failure　mode　to　be　precisely　evaluated.　This　may　not　be　realistic　in　real　applications.　In　this　paper　we　treat　the　risk　factors　O,　S　and　D　as　fuzzy　variables　and　evaluate　them　using　fuzzy　linguistic　terms　and　fuzzy　ratings.　As　a　result,　fuzzy　risk　priority　numbers　(FRPNs)　are　proposed　for　prioritization　of　failure　modes.　The　FRPNs　are　defined　as　fuzzy　weighted　geometric　means　of　the　fuzzy　ratings　for　O,　S　and　D,　and　can　be　computed　using　alpha-level　sets　and　linear　programming　models.　For　ranking　purpose,　the　FRPNs　are　defuzzified　using　centroid　defuzzification　method,　in　which　a　new　centroid　defuzzification　formula　based　on　alpha-level　sets　is　derived.　A　numerical　example　is　provided　to　illustrate　the　potential　applications　of　the　proposed　fuzzy　FMEA　and　the　detailed　computational　process　of　the　FRPNs.　©　2007　Elsevier　Ltd.　All　rights　reserved.