Existing　research　on　acceptability　of　pairwise　interval　comparison　matrices　focuses　on　acceptable　consistency　by　controlling　their　inconsistency　levels　to　within　a　certain　threshold.　However,　a　perfectly　consistent　but　highly　indeterminate　interval　comparison　matrix　can　be　unacceptable　as　it　contains　little　(sometimes　no)　useful　decision　information.　This　paper　first　analyzes　the　current　definition　of　acceptable　consistency　for　interval　multiplicative　comparison　matrices　(IMCMs)　and　shows　its　technical　deficiencies.　We　then　introduce　a　new　notion　of　acceptable　IMCMs,　considering　both　inconsistency　and　indeterminacy　levels　in　IMCMs.　A　geometric-mean-based　index　is　proposed　to　measure　the　indeterminacy　ratio　of　an　IMCM,　and　useful　properties　are　derived　for　consistent　IMCMs　and　acceptable　IMCMs.　An　indeterminacy-ratio　and　geometric　mean-based　transformation　equation　is　subsequently　put　forward　to　convert　normalized　acceptable　interval　multiplicative　weights　into　an　acceptable　IMCM　with　consistency.　By　introducing　an　auxiliary　constraint,　a　logarithmic　least　square　model　is　established　to　generate　interval　multiplicative　weights　from　acceptable　IMCMs.　A　geometric-mean-based　possibility　degree　formula　is　designed　to　compare　and　rank　normalized　interval　multiplicative　weights.　Two　numerical　examples　are　presented　to　illustrate　how　to　utilize　the　proposed　framework.　(C)　2015　Elsevier　B.V.　and　Association　of　European　Operational　Research　Societies　(EURO)　within　the　International　Federation　of　Operational　Research　Societies　(IFORS).　All　rights　reserved.