Multi-attribute　decision-making　problems　under　the　trapezoidal　fuzzy　neutrosophic　numbers　environment　are　complex,　particularly　when　the　attribute　value　data　are　incomplete,　and　the　attribute　weight　is　completely　unknown.　As　a　solution,　this　study　proposes　a　decision-making　method　based　on　information　entropy　and　grey　theory.　First,　regarding　the　problem　of　attribute　value　incompleteness　in　the　decision　matrix,　a　method　of　defining　the　missing　information　using　trapezoidal　fuzzy　neutrosophic　numbers　is　proposed,　which　is　simpler　and　more　reasonable　than　the　traditional　method　of　complements.　Regarding　the　problem　of　completely　unknown　attribute　weights,　the　definition　of　new　trapezoidal　fuzzy　neutrosophic　entropy　is　proposed　and　used　to　determine　the　attribute　weight.　Thereafter,　the　grey　relation　analysis　method　of　grey　theory　is　used　to　rank　alternatives　and　select　the　best　one.　Finally,　an　illustrative　example　about　typhoon　disaster　assessment　is　presented　to　show　the　feasibility　and　effectiveness　of　the　proposed　method.　Finally,　the　advantages　of　the　proposed　method　are　illustrated　by　comparison　with　other　methods　from　multiple　aspects.　©　2013　IEEE.