Attitude- and cost-driven consistency optimization model for decision-making with probabilistic linguistic preference relation

Probabilistic linguistic term set (PLTS) conveys the preference for a linguistic term by assigning a probability distribution, which can more correctly and flexibly reflect the decision-maker (DM)'s evaluation information and make the decision outcome more scientific and rational. Probabilistic linguistic preference relation (PLPR) allows the DM to represent decision information for pairwise comparison of alternatives with PLTS, allowing a more comprehensive representation of the DM's valid preferences. Consistency is essential in the preference decisionmaking process and directly influences the dependability of the final results. Therefore, this paper develops a minimum cost consistency adjustment mechanism based on attitudes and emotions for solving the decisionmaking problem with PLPR. Firstly, a new PLTS normalization model is proposed to handle the unknown information, considering the DM's preferred attitude and emotional tone. Secondly, the expected parametric multiplicative consistency index for PLPR is defined, and parameter settings improve the flexibility and relevance of the consistency. Then, the concepts of linguistic hesitancy, probabilistic uncertainty, and probabilistic incompleteness are defined for the PLTS that can reflect the psychological characteristics of DMs' hesitancy; they are then used to measure hesitation and unit consistency adjustment costs. Next, a new distance measure is established between the two PLTSs to measure the difference between the preference information. Subsequently, a direction-guided minimum cost consistency optimization model with unacceptable consistency is constructed for the PLPR. Finally, the usefulness of the suggested decision-making method with PLPR is tested using a numerical example of talent selection, and parametric sensitivity analysis and comparative analysis are utilized to show the benefits of the suggested methodology.