The　main　objective　of　this　paper　is　to　develop　a　new　ranking　methodology　for　solving　matrix　games　with　intuitionistic　fuzzy　payoffs　in　terms　of　a　value　and　ambiguity　of　triangular　intuitionistic　fuzzy　numbers　(TIFNs).　In　order　to　obtain　an　equilibrium　solution　of　this　matrix　game,　we　construct　two　auxiliary　TIFN　programming　models　that　are　transformed　into　bi-objective　linear　programming　models　which　are　solved　by　a　lexicographic　methodology.　The　validity　and　applicability　of　the　proposed　methodology　in　this　paper　are　illustrated　with　a　numerical　example.