Multi-stage consistency optimization algorithm for decision making with incomplete probabilistic linguistic preference relation

Abstract 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 model is proposed for improving the consistency of the InPLPR by minimizing the information distortion and the number of adjusted linguistic terms, which can also minimize the uncertainty of the relationship as small as possible. Afterward, to rank all the alternatives, a mathematical model for deriving the priority weights of the alternatives is constructed and solved, which can obtain the priority weight conveniently and quickly. A decision-making algorithm based on the consistency of the InPLPR is developed, which involves estimating missing information, checking and improving the consistency, and ranking the alternatives. Finally, a numerical case involving the selection of excellent students is presented to demonstrate the application of the proposed algorithm, and a detailed validation test and comparative analysis are presented to highlight the advantages of the proposed algorithm.