Consensus　reaching　processes　(CRPs)　have　been　required　to　assure　the　consensus　in　large　scale　group　decision　making　(LSGDM).　Opinion　reliability　detection　has　been　demanded　to　ensure　the　trustworthiness　of　the　original　information　and　different　information　modeling　approaches　have　facilitated　it　in　which　two　dimensional　linguistic　(TDL)　information　has　an　outstanding　place.　The　reliability　degree　of　original　opinions　elicited　by　TDL　expressions　is　often　given　in　advance　as　subjective　evaluation,　and　after　adjustment　during　CRP,　the　reliability　of　the　adjusted　opinions　is　often　neglected　especially　for　automatic　CRP,　which　may　lead　to　unreliable　decisions.　In　real　decision　making,　considering　the　interest　of　decision　makers　(DMs)　themselves,　the　self-assessment　of　the　DMs　on　the　reliability　of　the　given　opinions　could　be　easily　manipulated　by　DMs.　To　reduce　the　subjectivity　of　the　decision　making,　we　propose　a　method　to　obtain　objectively　the　reliability　of　the　adjusted　opinions　through　a　two-stage　minimum　cost　consensus　model　based　on　2-tuple　linguistic　additive　preference　relations.　Firstly,　a　support　degree　(SD)-based　clustering　method　will　be　developed　for　classifying　DMs　into　several　subgroups　to　make　more　manageable　the　large　number　of　DMs.　Subsequently,　a　two-stage　minimum　adjustment　consensus　model　will　be　presented　to　improve　the　consensus　level　(CL)　gradually.　Eventually,　the　adjusted　opinions　will　be　presented　as　two-dimension　2-tuple　linguistic　(TD2L)　information.　A　comparative　performance　analysis　of　this　CRP　based　LSGDM　approach　will　be　provided　to　show　its　effectiveness.　©　2020　Elsevier　Ltd