This　paper　develops　a　novel　triangular　fuzzy　noncooperative-cooperative　biform　game　framework　to　examine　the　formation　of　a　bilateral　link　network　and　addresses　profit　allocations　with　triangular　fuzzy　coalition　characteristic　values.　This　triangular　fuzzy　noncooperative-cooperative　biform　game　consists　of　four　elements:　nodes　(or　players),　link　modes　(or　strategy　choice),　network　formation　(or　coalitions)　and　information　flow　(or　triangular　fuzzy　coalition　characteristic　functions),　and　contains　both　the　triangular　fuzzy　noncooperative　and　cooperative　components.　The　payoffs　are　not　directly　given　a　priori　in　the　triangular　fuzzy　noncooperative　part,　but　are　determined　by　solving　the　triangular　fuzzy　cooperative　part.　To　solve　the　triangular　fuzzy　cooperative　games,　we　redefine　the　Banzhaf　values　under　the　triangular　fuzzy　numbers　case.　In　addition,　we　establish　the　general　existence　conditions　of　the　Nash　equilibrium　in　the　triangular　fuzzy　noncooperative-cooperative　biform　game.　Finally,　numerical　example　is　used　to　verify　the　effectiveness,　applicability　and　complexity　of　the　proposed　models　and　methods,　and　this　framework　provides　a　new　way　to　solve　the　problems　of　both　strategy　choices　and　profits　allocation.　Copyright　©2022　Control　and　Decision.