Most　linguistic-based　approaches　to　multi-attribute　group　decision　making　(MAGDM)　use　symmetric,　uniformly　distributed　sets　of　additive　linguistic　terms　to　express　the　opinions　of　decision　makers.　However,　in　reality,　there　are　also　some　problems　that　require　the　use　of　asymmetric,　uneven,　i.e.,　non-equilibrium,　multiplicative　linguistic　term　sets　to　express　the　evaluation.　The　purpose　of　this　paper　is　to　propose　a　new　approach　to　MAGDM　under　multiplicative　linguistic　information.　The　aggregation　of　linguistic　data　is　an　important　component　in　MAGDM.　To　solve　this　problem,　we　define　a　chi-square　for　measuring　the　difference　between　multiplicative　linguistic　term　sets.　Furthermore,　the　linguistic　generalized　weighted　logarithm　multiple　averaging　(LGWLMA)　operator　and　linguistic　generalized　ordered　weighted　logarithm　multiple　averaging　(LGOWLMA)　operator　are　proposed　based　on　chi-square　deviation.　On　the　basis　of　the　proposed　two　operators,　we　develop　a　novel　approach　to　GDM　with　multiplicative　linguistic　term　sets.　Finally,　the　evaluation　of　transport　logistics　enterprises　is　developed　to　illustrate　the　validity　and　practicality　of　the　proposed　approach.