In　view　of　the　characteristics　of　the　fuzzy　nature　of　real　economic　management　decision　making　environment　and　conditions,　this　paper　studies　a　class　of　cooperative　games　that　the　values　of　coalitions　are　expressed　with　trapezoidal　fuzzy　numbers.　The　main　purpose　of　this　paper　is　to　develop　a　kind　of　least　square　optimization　method　for　solving　trapezoidal　fuzzy　number　cooperative　games.　Firstly,　according　to　the　concept　of　the　trapezoidal　fuzzy　numbers＇　distance　(square)　and　the　least　square　method,　an　optimized　mathematical　model　is　proposed　by　considering　that　players　in　coalitions　try　to　guarantee　their　payoffs＇　sums　being　as　close　to　the　coalitions＇　values　as　possible.　Then　all　players＇　analytical　formulas　of　trapezoidal　fuzzy　number　payoffs　are　determined　by　the　optimized　mathematical　model.　Finally,　some　important　properties　of　the　least　square　solutions　are　discussed.~The　new　model　is　proposed　to　avoid　the　uncertainty　expansion　caused　by　the　trapezoidal　fuzzy　number　subtraction,　which　can　provide　a　new　theoretical　perspective　and　practical　tool　for　solving　the　trapezoidal　fuzzy　number　cooperative　games.　©　2019,　Editorial　Office　of　Control　and　Decision.　All　right　reserved.