The　probabilistic　interval-valued　hesitant　fuzzy　sets　(PIVHFSs),　being　able　to　generalize　interval-valued　hesitant　fuzzy　sets　embedded　with　the　decision　makers　(DMs)’　preferences　for　different　elements,　can　depict　uncertain　decision　information　completely　and　precisely.　Therefore,　with　this　study,　we　propose　an　extended　Elimination　and　Choice　Translating　Reality　(ELECTRE)　III　method　based　on　regret　theory　and　Borda　rule　under　a　PIVHFS　environment,　which　has　the　advantage　of　considering　the　regret　psychology　of　the　DMs　and　subordinate　ranking　orders.　Using　the　proposed　methodology,　a　fuzzy　bidirectional　projection　measure　is　developed　to　overcome　the　shortcoming　of　unidirectional　projection.　The　proposed　method　is　validated　by　two　numerical　examples,　and　the　effectiveness　of　the　method　is　demonstrated　through　sensitivity　and　comparative　analyses.　©　2023　Elsevier　Ltd