Multi-attribute　group　decision　making　(MAGDM)　problems　widely　exist　in　our　daily　life.　In　such　problems,　multiple　decision　makers　(DMs)　are　involved　and　elicit　their　evaluations　to　assess　a　set　of　possible　alternatives.　Their　complexity　usually　implies　to　deal　with　uncertain　contexts　and　the　use　of　linguistic　preference　modelling　for　the　elicited　assessments　has　been　common.　Linguistic　distribution　assessments　(LDAs)　applied　to　MAGDM,　involving　several　linguistic　terms　associated　with　their　symbolic　proportions,　have　been　effective　to　describe　such　assessments.　However,　to　ensure　a　reasonable　decision　making　result,　the　consistency　of　LDAs　should　be　investigated　and　a　corresponding　MAGDM　method　proposed.　This　paper　proposes　a　MAGDM　method　based　on　regret　theory,　not　only　to　take　the　psychological　behaviors　of　DMs　into　account,　but　also　to　reflect　the　consistency　of　assessments.　Hence,　the　additive　regret　preference　relation　is　firstly　defined　and　then　four　algorithms　are　devised　to　improve　the　consistency　of　assessments.　On　this　basis,　two　weighting　determination　models　are　built　to　calculate　the　weights　of　attributes　and　DMs　respectively.　Furthermore,　alternatives　can　be　ranked　according　to　their　overall　synthetic　values.　The　proposed　MAGDM　method　is　applied　to　an　emergency　assistance　area　selection　problem　and　its　result　verifies　the　feasibility　and　effectiveness　of　the　proposal.