For　the　multiple　attribute　group　decision　making　(MAGDM)　problem,　in　which　the　attribute　weights　are　unknown　and　the　attribute　value　of　alternatives　is　in　the　form　of　a　trapezoidal　fuzzy　neutrosophic　number,　this　paper　proposes　two　multiple　attribute　group　decision　making　methods:　one　based　on　the　trapezoidal　fuzzy　neutrosophic　number　hybrid　averaging　(TrFNNHA)　operator,　and　the　other　based　on　the　technique　for　order　performance　by　similarity　to　ideal　solution　(TOPSIS)　method.　First,　the　attribute　weights　are　obtained　using　the　truth　favorite　relative　expected　value,　and　the　distance　measure　defined　using　the　cosine　similarity　measure.　Next,　a　proposed　trapezoidal　fuzzy　neutrosophic　number　ordered　weighted　arithmetic　averaging　(TrFNNOWAA)　operator　and　a　proposed　trapezoidal　fuzzy　neutrosophic　number　hybrid　weighted　arithmetic　averaging　(TrFNNHWAA)　operator　are　used　to　aggregate　the　trapezoidal　fuzzy　neutrosophic　information.　Then,　the　score　and　accuracy　functions　of　a　trapezoidal　neutrosophic　number　are　used　to　rank　the　alternatives　and　obtain　the　best　alternative　in　a　trapezoidal　fuzzy　neutrosophic　environment.　In　addition,　an　extended　TOPSIS　method　is　also　proposed　to　deal　with　trapezoidal　fuzzy　neutrosophic　information.　An　illustrative　example　and　sensitivity　analysis　demonstrate　the　applicability　and　effectiveness　of　the　proposed　group　decision　making　methods.　©　2017　-　IOS　Press　and　the　authors.　All　rights　reserved.