The　safety　of　agricultural　products　has　always　been　a　matter　of　great　concern　to　people.　To　address　this　concern,　many　blockchain-based　agricultural　product　traceability　systems　(BAPTSs)　have　been　constructed.　The　implementation　of　such　systems　necessitates　the　selection　of　an　appropriate　design　scheme.　However,　due　to　the　diversity　of　agricultural　products　and　the　uncertainty　of　the　environment,　selecting　an　adequate　design　scheme　for　BAPTS　is　a　difficult　task　for　decision-makers.　Because　the　q-rung　orthopair　fuzzy　(q-ROF)　set　can　dynamically　delineate　the　space　of　uncertain　information,　this　paper　proposes　a　decision　algorithm　for　selecting　a　design　scheme　for　BAPTS　using　the　q-ROF　set.　Herein,　we　first　combine　the　Muirhead　mean　operator　and　power　operator　to　develop　the　q-ROF　power　Muirhead　Mean　(q-ROFPMM)　operator　and　the　q-ROF　weighted　power　Muirhead　Mean　(q-ROFWPMM)　operator.　Then,　we　investigate　several　properties　of　the　proposed　operators.　Further,　we　construct　a　novel　multi-criteria　decision-making　framework　for　evaluating　and　selecting　the　design　scheme　for　BAPTS　based　on　the　q-ROFWPMM　operator.　Next,　a　case　study　on　BAPTS　selection　is　presented　to　validate　our　method.　Finally,　the　results　of　sensitivity　and　comparative　analyses　are　provided　to　verify　the　efficiency　and　accuracy　of　our　method.　The　results　show　that　our　method　can　effectively　address　the　issues　of　BAPTS　evaluation　and　selection,　capture　the　relationships　between　any　number　of　criteria,　and　eliminate　the　negative　effects　of　abnormal　expert　evaluation　values　on　decision-making　results.　©　2020　Elsevier　Ltd