In　recent　years,　typhoon　disasters　have　occurred　frequently　and　the　economic　losses　caused　by　them　have　received　increasing　attention.　This　study　focuses　on　the　evaluation　of　typhoon　disasters　based　on　the　interval　neutrosophic　set　theory.　An　interval　neutrosophic　set　(INS)　is　a　subclass　of　a　neutrosophic　set　(NS).　However,　the　existing　exponential　operations　and　their　aggregation　methods　are　primarily　for　the　intuitionistic　fuzzy　set.　So,　this　paper　mainly　focus　on　the　research　of　the　exponential　operational　laws　of　interval　neutrosophic　numbers　(INNs)　in　which　the　bases　are　positive　real　numbers　and　the　exponents　are　interval　neutrosophic　numbers.　Several　properties　based　on　the　exponential　operational　law　are　discussed　in　detail.　Then,　the　interval　neutrosophic　weighted　exponential　aggregation　(INWEA)　operator　is　used　to　aggregate　assessment　information　to　obtain　the　comprehensive　risk　assessment.　Finally,　a　multiple　attribute　decision　making　(MADM)　approach　based　on　the　INWEA　operator　is　introduced　and　applied　to　the　evaluation　of　typhoon　disasters　in　Fujian　Province,　China.　Results　show　that　the　proposed　new　approach　is　feasible　and　effective　in　practical　applications.　©　2018　by　the　authors.