Purpose　The　purpose　of　this　paper　is　to　develop　a　multi-criterion　group　decision-making　(MCGDM)　method　by　combining　the　regret　theory　and　the　Choquet　integral　under　2-tuple　linguistic　environment　and　apply　the　proposed　method　to　deal　with　the　supplier　selection　problem.　Design/methodology/approach　When　making　a　decision,　the　decision-maker　is　more　willing　to　choose　the　alternative(s)　which　is　preferred　by　the　experts　so　as　to　avoid　the　regret.　At　the　same　time,　the　correlative　relationships　among　the　criterion　set　can　be　sufficiently　described　by　the　fuzzy　measures,　later　the　evaluations　of　a　group　of　criteria　can　be　aggregated　by　means　of　the　Choquet　integral.　Hence,　the　authors　cope　with　the　MCGDM　problems　by　combining　the　regret　theory　and　the　Choquet　integral,　where　the　fuzzy　measures　of　criteria　are　partly　known　or　completely　unknown　and　the　evaluations　are　expressed　by　2-tuples.　The　vertical　and　the　horizontal　regret-rejoice　functions　are　defined　at　first.　Then,　a　model　aiming　to　determine　the　missing　fuzzy　measures　is　constructed.　Based　on　which,　an　MCGDM　method　is　proposed.　The　proposed　method　is　applied　to　tackle　a　practical　decision-making　problem　to　verify　its　feasibility　and　the　effectiveness.　Findings　The　vertical　and　the　horizontal　regret-rejoice　functions　are　defined.　The　relationships　of　the　fuzzy　measures　are　expressed　by　the　sets.　A　model　is　built　for　determining　the　fuzzy　measures.　Based　on　which,　an　MCGDM　method　is　proposed.　The　results　show　that　the　proposed　method　can　solve　the　MCGDM　problems　within　the　context　of　2-tuple,　where　the　decision-maker　avoids　the　regret　and　the　criteria　are　correlative.　Originality/value　The　paper　proposes　an　MCGDM　method　by　combining　the　regret　theory　and　the　Choquet　integral,　which　is　suitable　for　dealing　with　a　variety　of　decision-making　problems.