With　the　increasing　complexity　of　the　decision　environment,　the　fuzzy　theory　has　attracted　the　extensive　attention　of　scholars.　Probabilistic　interval-valued　hesitant　fuzzy　set,　as　a　complex　ambiguous　information　representation　tool,　dedicates　to　depict　uncertain　information　as　complete　as　possible.　Thus,　this　paper　proposes　a　probabilistic　interval-valued　hesitant　fuzzy　gained　and　lost　dominance　score　method　based　on　regret　theory　and　interval　evidential　reasoning　approach.　In　view　of　the　uncertainties　in　evaluations,　the　interval　evidential　reasoning　approach　is　an　effective　tool　to　deal　with　the　fuzziness　and　ignorance,　which　is　first　applied　in　probabilistic　interval-valued　hesitant　fuzzy　information　in　this　paper.　Besides,　an　interval　projection　measure　is　proposed　to　consider　both　distance　and　direction　simultaneously,　so　as　to　avoid　the　problem　of　information　losses　in　the　decision　process.　On　this　basis,　a　novel　regret-rejoice　function　is　developed.　Then,　an　extended　gained　and　lost　dominance　score　method　based　on　regret　theory　and　interval　evidential　reasoning　approach　is　developed,　which　considers　the　regret　avoidance　behavior　of　experts.　Finally,　a　case　study　on　supplier　selection　of　epidemic　prevention　products　is　applied　to　elucidate　and　illustrate　the　application　of　the　proposed　method　in　this　paper.