The　aim　of　this　paper　is　to　develop　an　effective　methodology　for　solving　matrix　games　with　payoffs　of　intuitionistic　fuzzy　sets　(IFSs).　In　this　methodology,　a　new　ranking　order　relation　of　IFSs　is　proposed　and　the　concept　of　Pareto　Nash　equilibrium　solutions　of　matrix　games　with　IFS　payoffs　is　firstly　defined.　It　is　proven　that　the　solutions　of　matrix　games　with　IFS　payoffs　are　equivalent　to　those　of　a　pair　of　bi-objective　programming　models.　The　models　and　method　proposed　in　this　paper　are　illustrated　with　a　numerical　example　and　compared　with　other　methods　to　show　the　validity,　applicability　and　superiority.　©　Springer　Nature　Singapore　Pte　Ltd.　2017.