The　aim　of　this　paper　is　to　develop　a　new　methodology　for　solving　bi-matrix　games　in　which　goals　are　regarded　as　intuitionistic　fuzzy　(IF)　sets　(IFSs)　and　payoffs　are　expressed　with　triangular　IF　numbers　(TIFNs).　In　this　methodology,　a　new　ranking　method　of　TIFNs　is　proposed　and　the　concept　of　IF　inequalities　is　interpreted.　An　IF　non-linear　programming　model　is　constructed　to　obtain　the　solution　for　such　a　type　of　bi-matrix　games.　Then　utilizing　these　IF　inequalities　and　the　ranking　method　of　TIFNs　proposed　in　this　paper,　the　solution　of　any　bi-matrix　game　with　goals　of　IFSs　and　payoffs　of　TIFNs　can　be　transformed　into　a　crisp　non-linear　programming　problem.　It　is　shown　that　the　bi-matrix　game　with　goals　of　IFSs　and　payoffs　of　TIFNs　is　a　generalization　of　the　bi-matrix　game　with　goals　of　fuzzy　sets　and　payoffs　of　triangular　fuzzy　numbers.　The　method　proposed　in　this　paper　is　demonstrated　with　a　numerical　example　of　commerce　retailers＇　strategy　choice　problem.