Purpose:　Three-parameter　interval　grey　numbers　(TPIGNs)　have　been　extensively　studied　as　an　extended　form　of　interval　numbers.　However,　most　existing　TPIGN　multi-attribute　decision-making　methods　only　consider　the　similarity　of　positions,　ignore　the　similarity　of　developmental　directions　and　focus　primarily　on　static　evaluation.　To　address　these　limitations,　in　this　study,　the　authors　propose　a　dynamic　technique　for　order　preference　by　similarity　to　an　ideal　solution　(TOPSIS)　based　on　modified　Jaccard　similarity　and　angle　similarity　for　TPIGNs.　Design/methodology/approach:　First,　the　authors　extend　Jaccard　similarity　to　a　TPIGN　environment　to　represent　positional　similarity.　A　simple　example　is　provided　to　illustrate　the　limitations　of　the　traditional　Jaccard　similarity.　Then,　the　authors　introduce　an　angle　similarity　measure　to　represent　developmental　directional　similarity.　Finally,　a　dynamic　TOPSIS　model　is　constructed　by　incorporating　time-series　data　into　conventional　two-dimensional　static　data.　Stage　weights　are　obtained　by　an　objective　function　designed　to　maximize　the　amount　and　minimize　the　fluctuation　of　decision　information.　A　quadratic　weighting　method　is　adopted　to　derive　the　overall　evaluation　value　of　alternatives.　Findings:　To　evaluate　the　effectiveness　of　the　proposed　method,　this　study　takes　the　pre-assessment　of　ice　disaster　and　the　selection　of　cooperative　enterprises　as　examples.　The　authors　then　provide　the　results　of　comparative　and　sensitivity　analyses,　which　demonstrate　the　effectiveness　and　flexibility　of　the　proposed　method.　Originality/value:　The　proposed　TOPSIS　method　in　a　TPIGN　environment　can　take　a　more　holistic　and　dynamic　perspective　for　decision-making,　which　helps　mitigate　the　limitations　of　single-perspective　or　static　evaluations.　©　2023,　Emerald　Publishing　Limited.