Multi-granularity　probabilistic　linguistic　Z-number　(PLZN)　is　an　effective　and　flexible　tool　for　expressing　expert　opinions.　For　group　decision-making　(GDM)　problems　with　multi-granularity　PLZN　preference　relations　(PLZNPRs),　this　paper　proposes　a　GDM　method　based　on　data　envelopment　analysis　cross-evaluation　(DEA-CE)　model　and　expert　credibility.　First,　as　the　foundation　for　solving　GDM　problems　with　multi-granularity　PLZNPRs,　this　paper　reveals　the　inadequacies　of　existing　methods　on　transformation　and　comparison　between　multi-granularity　PLZNs　through　arithmetic　examples.　After　analyzing　these　inadequacies,　this　paper　proposes　the　novel　transformation　and　comparison　methods　with　better　performances.　Second,　to　obtain　the　priorities　of　multi-granularity　PLZNPRs　more　efficiently,　DEA-CE　model　is　introduced　and　the　effectiveness　of　introducing　DEA-CE　model　is　demonstrated.　The　superiority　of　introducing　DEA-CE　model　is　that　it　requires　no　further　adjustment　of　preference　relations　at　any　consistency　level,　which　helps　to　maximize　the　retention　of　original　information.　Third,　the　subjective　expert　weights　determined　based　on　realistic　situations　are　objectively　adjusted　using　the　expert　credibility　calculated　according　to　the　information　quality,　making　the　results　more　reasonable.　Finally,　this　paper　illustrates　by　two　case　examples　that　the　proposed　model　can　be　well　adapted　to　GDM　problems　with　all　sizes,　regardless　of　the　numbers　of　decision　variables　and　experts.