In　actual　decision　making,　there　are　many　multiple　criteria　decision　making　(MCDM)　problems　with　prioritization　and　interaction　among　the　criteria.　In　this　paper,　we　proposed　a　novel　method　to　handle　the　intuitionistic　fuzzy　MCDM　problems　with　weakly　ordered　prioritization　and　interaction　among　the　criteria.　First,　we　presented　some　novel　Einstein　operations　of　intuitionistic　fuzzy　sets　(IFSs),　which　could　capture　the　relationship　between　non-membership　and　membership　functions　of　various　IFSs.　Then,　we　proposed　a　novel　operator　called　prioritized　interactive　Choquet　(PIC)　operator　based　on　fuzzy　measure,　generalized　prioritized　measure,　and　Choquet　integral.　Meanwhile,　three　fundamental　features　of　this　operator　were　discussed.　Besides,　we　combined　the　PIC　operator　and　Einstein　operations　to　IFSs,　and　proposed　the　intuitionistic　fuzzy　prioritized　interactive　Einstein　Choquet　(IFPIEC)　operator,　which　could　consider　the　prioritization　and　interaction　among　the　criteria.　Additionally,　we　utilized　O＇Hagan＇s　maximum　entropy　to　obtain　the　quantity　of　each　priority　level　in　the　generalized　prioritized　measure.　Finally,　the　detailed　decision　making　steps　for　the　intuitionistic　fuzzy　MCDM　problems　with　weakly　ordered　prioritization　and　interaction　were　developed,　and　two　practical　cases　were　given　to　check　the　created　approach　and　to　illustrate　its　validity　and　superiority.