The　aim　of　this　paper　is　to　develop　a　newmethodology　for　solving　matrix　games　with　payoffs　of　Atanassov＇s　intuitionistic　fuzzy　(I-fuzzy)　numbers.　In　this　methodology,　we　define　the　concepts　of　I-fuzzy　numbers　and　the　value-index　and　ambiguity-index　and　develop　a　difference-index-based　ranking　method,　which　is　proven　to　be　a　total　order.　By　doing　this,　the　parameterized　non-linear　programming　models　are　derived　from　a　pair　of　auxiliary　I-fuzzy　mathematical　programming　models,　which　are　used　to　determine　solutions　of　matrix　games　with　payoffs　of　I-fuzzy　numbers.　The　validity　and　applicability　of　the　models　and　method　proposed　in　this　paper　are　illustrated　with　a　practical　example.