Q-rung　orthopair　fuzzy　set　(q-ROFS)　is　a　powerful　tool　to　describe　uncertain　information　in　the　process　of　subjective　decision-making,　but　not　express　vast　objective　phenomenons　that　obey　normal　distribution.　For　this　situation,　by　combining　the　q-ROFS　with　the　normal　fuzzy　number,　we　proposed　a　new　concept　of　q-rung　orthopair　normal　fuzzy　(q-RONF)　set.　Firstly,　we　defined　the　conception,　the　operational　laws,　score　function,　and　accuracy　function　of　q-RONF　set.　Secondly,　we　presented　some　new　aggregation　operators　to　aggregate　the　q-RONF　information,　including　the　q-RONF　weighted　operators,　the　q-RONF　ordered　weighted　operators,　the　q-RONF　hybrid　operator,　and　the　generalized　form　of　these　operators.　Furthermore,　we　discussed　some　desirable　properties　of　the　above　operators,　such　as　monotonicity,　commutativity,　and　idempotency.　Meanwhile,　we　applied　the　proposed　operators　to　the　multi-attribute　decision-making　(MADM)　problem　and　established　a　novel　MADM　method.　Finally,　the　proposed　MADM　method　was　applied　in　a　numerical　example　on　enterprise　partner　selection,　the　numerical　result　showed　the　proposed　method　can　effectively　handle　the　objective　phenomena　with　obeying　normal　distribution　and　complicated　fuzzy　information,　and　has　high　practicality.　The　results　of　comparative　and　sensitive　analysis　indicated　that　our　proposed　method　based　on　q-RONF　aggregation　operators　over　existing　methods　have　stronger　information　aggregation　ability,　and　are　more　suitable　and　flexible　for　MADM　problems.