In　this　study,　we　provide　an　expertise-based　weight　allocation　approach　for　heterogeneous　experts　with　incomplete　linguistic　preference　relations　(ILPRs)　in　heterogeneous　group　decision-making　(HGDM).　Based　on　the　uninorm　consistency　(U-consistency)　theory,　this　paper　proposes　a　new　four-way　iteration　step　to　estimate　the　missing　preference　values　so　as　to　preserve　the　original　information　as　much　as　possible.　After　obtaining　the　complete　linguistic　preference　relations　that　satisfies　reciprocity　and　boundedness,　the　discrimination　indicator　is　introduced　to　measure　the　expertise　level　of　heterogeneous　experts,　and　its　definition　and　calculation　method　in　linguistic　context　is　provided.　In　contrast　to　complete　preference　information,　when　assigning　weights　for　heterogeneous　experts　with　ILPRs,　the　contradictory　relationship　between　their　inconsistency　and　incompleteness,　which　had　been　proved　by　numerical　simulation,　exists　and　needs　solving.　Then,　using　defined　discrimination,　inconsistency　and　incompleteness,　we　propose　a　New-Index　and　a　weight　allocation　method,　the　validity　of　which　had　been　illustrated　by　the　numerical　example,　to　measure　objectively　heterogeneous　experts＇　expertise.　Considering　these　three　indicators,　the　proposed　weight　is　more　reasonable　than　existent　weight　allocation　methods　with　single　indicator.　(C)　2018　Elsevier　B.V.　All　rights　reserved.