The　probabilistic　linguistic　term　set　(PLTS)　shows　great　superiority　in　expressing　decision-makers’　opinions.　The　multi-attribute　decision-making　(MADM)　problem　under　a　PLTS　environment　has　gained　attention　from　numerous　scholars.　However,　the　majority　of　current　studies　are　not　precise　enough　in　capturing　information　on　PLTS.　To　address　this　problem,　this　paper　presents　a　preference　ranking　organization　method　for　enrichment　of　evaluations　(PROMETHEE)　based　on　the　redefined　PLTS　and　novel　score　function　to　solve　MADM　problems　under　a　PLTS　environment.　First,　an　asymmetric　normalized　PLTS　based　on　prospect　theory　(ANPLTSPT)　is　developed.　Compared　with　the　PLTS,　ANPLTSPT　offers　a　more　realistic　portrayal　of　decision-makers’　psychological　state　while　ensuring　the　superiority　of　the　PLTS.　Second,　regarding　the　structural　complexity　of　ANPLTSPT,　this　paper　attempts　to　simplify　the　computational　process　through　a　score　function　that　can　embody　the　characteristics　of　ANPLTSPT.　Inspired　by　previously　formulated　score　functions,　a　novel　score　function　called　Score-InInHe　is　developed,　the　corresponding　definitions　are　given,　and　some　further　properties　are　discussed.　With　the　support　of　the　proposed　Score-InInHe,　the　total　score　entropy　is　defined　and　an　objective　method　to　determine　the　attribute　weights　is　proposed.　Finally,　the　proposed　approach　is　applied　to　the　selection　of　a　green　supplier　and　the　determination　of　air　quality.　The　validity　and　realistic　applicability　of　the　proposed　approach　are　demonstrated　through　comparative　analyses　and　discussions.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.