<p>The aim of this paper is to propose a novel group decision-making (GDM) method that addresses expert weight uncertainty and efficiency interval estimation. Based on interval multiplicative probabilistic linguistic preference relations, this study combines entropy weight method, multiplicative data envelopment analysis (DEA) cross-efficiency and Bootstrap analysis to provide a more accurate and reliable GDM framework. First, logarithmic function is introduced into the entropy method to measure the fuzziness and hesitancy of preference matrix sufficiently and quantify the weight of expert information. Then, a multiplicative DEA cross-efficiency model is adopted for efficiency evaluation of the decision-making units. Logarithmic function is designed in this model to intuitively display efficiency differences. We further develop Bootstrap-DEA for efficiency correction, leveraging its statistical advantages to enhance the robustness and reliability of our GDM method. Finally, a numerical example and comparative analysis are provided to highlight the rationality and effectiveness of the proposed GDM method.</p>