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Multiplicative probabilistic linguistic preference relation (MPLPR) has been widely used by decision-makers (DMs) to tackle group decision-making (GDM) problems. However, due to the complexity of the decision-making circumstance and individual subjectivity of DMs, they often provide inconsistent MPLPRs which often lead to unreasonable decision results. To solve this problem, this paper investigates a novel approach to GDM with MPLPRs based on consistency improvement and upgraded multiplicative data envelopment analysis (DEA) cross-efficiency. First, the concept of sequential consistency of MPLPR is defined. Then, a consistency improvement algorithm is proposed, which can convert any unacceptable consistent MPLPR into an acceptable one. Furthermore, we use geometric averages to transform MPLPR into multiplicative preference relation (MPR). Meanwhile, considering the conservative psychology of DMs, an upgraded multiplicative DEA cross-efficiency model based on the pessimistic criterion is constructed, which can derive the priority vector of MPLPR. Therefore, we can obtain the rational ranking results for all alternatives. Finally, a case analysis of emergency logistics under COVID-19 is provided to illustrate the validity and applicability of the proposed approach. [ABSTRACT FROM AUTHOR]