The　interval-valued　Pythagorean　fuzzy　(IVPF)　sets,　describing　the　membership　and　non-membership　degrees　from　interval　values,　can　address　uncertain　information,　while　the　normal　fuzzy　number　(NFN)　can　depict　normal　distribution　information　in　anthropogenic　activity　and　natural　environment.　By　combining　the　advantages　of　both　operations,　in　this　study,　we　proposed　the　interval-valued　Pythagorean　normal　fuzzy　(IVPNF)　sets　by　introducing　the　NFN　into　IVPF　environment.　Firstly,　we　defined　the　conception,　the　operational　laws,　score　function,　accuracy　function　of　IVPNF　sets.　Secondly,　we　presented　four　information　aggregation　operators　to　aggregate　IVPNF　information,　including　the　IVPNF　weighted　averaging　(IVPNFWA)　operator,　IVPNF　weighted　geometric　(IVPNFWG)　operator,　the　generalized　IVPNFWA　operator,　and　the　generalized　IVPNFWG　operator.　In　addition,　we　analyzed　some　desirable　properties　of　monotonicity,　commutativity,　and　idempotency　for　the　proposed　four　operators.　Finally,　a　numerical　example　on　multi-attribute　decision-making　problem　is　given　to　verify　the　practicality　of　the　proposed　operators,　and　the　comparative　and　sensitive　analysis　are　used　to　show　the　effectiveness　and　flexibility　of　our　proposed　approach.