Linguistic　distribution　assessments　with　probabilistic　information　are　a　flexible　means　to　express　the　opinions　of　decision　makers　(DMs)　with　importance　degree　of　each　linguistic　term.　Therefore,　research　on　multi-attribute　group　decision　making　(MAGDM)　problems　with　linguistic　distribution　assessments　is　increasing.　However,　the　probability　distribution　is　usually　only　partially　known.　In　order　to　obtain　the　complete　probability　distribution　information,　we　propose　the　concept　of　stochastic　linguistic　term　(SLT)　with　the　aid　of　stochastic　analysis.　The　SLT　is　an　extension　of　general　linguistic　terms.　Linguistic　assessments　with　different　models　can　be　expressed　as　SLTs　with　complete　probability　distributions.　Then　the　weighted　averaging　operator　and　score　function　of　SLTs　are　presented.　Considering　the　psychological　behavior　of　DMs　in　decision　making,　we　combine　prospect　theory　and　SLTs　to　handle　uncertainty　in　MAGDM　problems.　Considering　2-tuple　aspirations　on　attributes,　a　new　MAGDM　method　with　stochastic　uncertainty　based　on　prospect　theory　under　linguistic　assessments　is　proposed.　Finally,　a　numeric　example　and　comparative　analysis　illustrate　the　effectiveness　and　feasibility　of　the　proposed　method.　©　2019　Elsevier　B.V.