The　purpose　of　this　paper　is　to　propose　the　novel　generalized　exponential　intuitionistic　fuzzy　entropy　(GIFE)　and　generalized　exponential　interval　valued　intuitionistic　fuzzy　entropy　(GIVIFE)　with　interval　area.　First,　we　propose　a　novel　GIFE.　Then　we　compare　the　new　GIFE　with　the　existing　intuitionistic　fuzzy　entropy　(IFE)　measures.　Second,　we　define　the　interval　area　and　the　new　axioms　for　the　interval　valued　intuitionistic　fuzzy　entropy　(IVIFE).　Third,　according　to　the　newly　defined　axioms　for　the　IVIFE,　we　use　the　interval　area　to　construct　the　new　GIVIFE.　Finally,　the　advantages　of　the　new　generalized　entropy　measures　are　compared　with　the　existing　IVIFE　measures　by　some　examples.　The　two　novel　generalized　exponential　entropy　measures　can　distinguish　the　special　cases　well.　We　have　the　conclusion　that　the　two　novel　generalized　entropy　measures　are　reasonable　and　more　flexible　than　the　existing　entropy.