Adding　an　additional　degree　of　non-membership,　K.　T.　Atanassov　introduced　the　concept　of　the　intuitionistic　fuzzy　(IF)　set　(IF-set),　which　has　rarely　been　applied　to　the　game　theory　yet.　The　aim　of　this　paper　is　to　develop　the　concept　and　methodology　of　matrix　games　with　IF-set　goals　in　which　goals　of　players　are　expressed　with　IF-sets　and　payoffs　are　expressed　with　real　numbers　rather　than　IF-sets.　In　this　methodology,　the　concepts　of　IF-set　goals　and　the　solutions　of　matrix　games　with　IF-set　goals　are　proposed.　It　is　proven　that　solutions　of　matrix　games　with　IF-set　goals　can　be　obtained　through　solving　the　developed　auxiliary　linear　programming　models,　which　are　the　generalization　of　matrix　games　with　fuzzy　goals.　The　proposed　methodology　is　illustrated　with　a　numerical　example.　Furthermore,　comparison　analysis　of　the　proposed　methodology　is　conducted　to　show　its　advantages　over　matrix　games　with　fuzzy　goals.