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Incomplete probabilistic linguistic term sets (InPLTSs) can effectively describe the qualitative pairwise judgment information in uncertain decision-making problems, making them suitable for solving real decision-making problems under time pressure and lack of knowledge. Thus, in this study, an optimization algorithm is developed for preference decision-making with the incomplete probabilistic linguistic preference relation (InPLPR). First, to fully investigate the ability of InPLTSs to express uncertain information, they are divided into two categories. Then, a two-stage mathematical optimization model based on an expected multiplicative consistency for estimating missing information is constructed, which can obtain the complete information more scientifically and effectively than some exiting methods. Subsequently, for the InPLPR with unacceptable consistency, a multi-stage consistency-improving optimization …