The　normalization　of　interval　and　fuzzy　weights　is　often　necessary　in　multiple　criteria　decision　analysis　(MCDA)　under　uncertainty,　especially　in　analytic　hierarchy　process　(AHP)　with　interval　or　fuzzy　judgements.　The　existing　normalization　methods　based　on　interval　arithmetic　and　fuzzy　arithmetic　are　found　flawed　and　need　to　be　revised.　This　paper　presents　the　correct　normalization　methods　for　interval　and　fuzzy　weights　and　offers　relevant　theorems　in　support　of　them.　Numerical　examples　are　examined　to　show　the　correctness　of　the　proposed　normalization　methods　and　their　differences　from　those　existing　normalization　methods.　©　2006　Elsevier　B.V.　All　rights　reserved.