The　complexity　of　the　socioeconomic　environment　means　that　it　is　challenging　to　make　decisions　that　rely　on　cognitive　information.　Decision　makers　normally　cannot　obtain　a　precise　or　sufficient　level　of　knowledge　about　the　problem　domain　and　hence　must　provide　multiple　answers　with　interval　values　to　depict　them.　This　makes　cognizing　and　decision　making　very　difficult.　To　address　this　issue,　this　paper　proposes　a　novel　cognitive　information-based　decision-making　algorithm　with　interval-valued　q-rung　picture　fuzzy　(IVq-RPtF)　numbers.　We　first　define　the　concept　of　the　IVq-RPtF　set,　including　the　basic　definition,　operational　laws,　a　score　function,　and　an　accuracy　function.　Considering　the　interrelationship　between　attributes,　we　then　present　the　IVq-RPtF　Heronian　mean　(IVq-RPtFHM)　operators　using　the　new　operational　laws.　Moreover,　we　discuss　the　properties　of　IVq-RPtFHM　operators,　such　as　monotonicity,　commutativity,　and　idempotency.　Finally,　we　use　a　numerical　example　to　verify　the　viability　of　the　proposed　method.　The　results　show　that　the　proposed　method　effectively　expresses　multiple　types　of　interval　cognitive　information.　The　sensitivity　analysis　of　the　parameters　shows　that　the　ranking　results　are　susceptible　to　parameter　changes,　but　regardless　of　how　the　parameters　change,　the　score　values　of　the　four　alternatives　in　our　example　are　in　the　range　of　[1.27,　1.66],　within　the　basic　scoring　range　of　[1.352–1.472]　for　the　four　alternatives.　Therefore,　our　proposed　method　based　on　IVq-RPtFHM　operators　has　a　stronger　information　aggregation　ability　than　other　methods.　Compared　with　other　methods,　the　proposed　cognitive　information-based　decision-making　algorithm　is　more　widely　applicable,　avoids　loss　of　cognitive　information,　and　conducts　a　reasonable　decision-making　process.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC　part　of　Springer　Nature.