This　paper　designs　a　consensus　reaching　process　(CRP)　with　minimum　adjustment　considering　that　decision　makers　(DMs)　have　a　tolerance　for　changing　their　preferences,　which　means　DMs　only　accept　the　adjustment　if　such　adjustment　fall　within　their　tolerance　interval.　In　addition,　two　consensus　rules　are　considered:　minimum　distance　between　original　and　adjusted　preferences,　and　minimum　number　of　adjusted　preferences.　Unlike　to　classical　CRP,　our　proposal　includes　a　reliability　detection　of　adjusted　preferences,　in　order　to　avoid　biased　solutions　because　of　the　inherent　subjectivity　of　group　decision-making　problems.　To　obtain　the　agreed　adjusted　opinions　and　their　reliability,　the　two-dimensional　2-tuple　linguistic　(TD2L)　information　is　used　in　which,　the　first　dimension　of　a　TD2L　is　2-tuple　linguistic　value　that　assess　the　adjusted　preference　and,　the　second　dimension　information　is　another　2-tuple　linguistic　value　assessing　the　reliability　degree　of　the　adjusted　preferences,　which　is　derived　according　to　similarity　between　adjusted　and　original　preferences.　Then　a　novel　comparison　method　for　TD2Ls　is　developed.　Finally,　an　illustrative　example　is　given　to　verify　the　proposed　method　and　the　results　show　that　the　approach　is　feasible　and　effective.