The　two-dimension　2-tuple　linguistic　(TD2L)　label,　based　on　the　traditional　2-tuple　linguistic　representation　model,　adds　another　2-tuple　linguistic　term　to　express　the　reliability　degree　of　the　assessments.　However,　the　reliability　degree　is　a　subjective　evaluation　on　reliability　of　the　given　assessments　and　variables　due　to　the　limitations　in　cognitions　and　the　complexity　of　decision　objects.　All　assessments　without　total　reliability　degree　are　viewed　as　uncertain　ones.　Based　on　this　idea,　this　paper　proposes　a　new　TD2L　representation　model　from　a　stochastic　perspective.　The　assessment　expressed　by　TD2L　is　a　variable　that　fluctuates　around　the　given　linguistic　term,　and　the　fluctuation　range　is　decided　by　the　reliability　of　the　assessment.　Therefore,　the　assessments　are　regarded　as　stochastic　variables,　where　the　expectancy　and　deviation　of　the　stochastic　variable　are　corresponding　to　the　first　dimension　and　the　second　dimension　information　of　TD2Ls,　respectively.　Consequently,　two　new　aggregation　functions　for　aggregating　TD2L　labels　based　on　the　algorithms　among　stochastic　variables　are　proposed.　In　addition,　the　comparison　and　similarity　measure　between　TD2L　labels　are　developed,　which　considers　the　relative　importance　of　the　two　dimensions　of　TD2L　labels.　Finally,　the　proposed　method　is　applied　to　an　investment　decision　of　medium　sized　enterprise　and　alternatives　ranking　is　provided　with　the　probability　of　superiority.　A　comparison　analysis　conducted　from　three　aspects　illustrates　the　effectiveness　of　the　proposed　method.　©　2022,　The　Author(s)　under　exclusive　licence　to　Taiwan　Fuzzy　Systems　Association.