The Research on Consistency Checking and Improvement of Probabilistic Linguistic Preference Relation Based on Similarity Measure and Minimum Adjustment Model

In the process of decision making, the probabilistic linguistic term set (PLTS) is a useful tool to express the evaluation information provided by decision makers (DMs). On the basis of PLTS, the probabilistic linguistic preference relation (PLPR) has been proposed, which can well describe the uncertainty of preferences when experts conduct pairwise comparison between any two alternatives. The consistency analysis is an essential process to check whether the preferences are reasonable and logical. For the consistency checking and improvement of PLPR, some methods have been developed to conduct the work. However, the previous methods seldom consider whether the information of original preferences is distorted after the adjustment of inconsistency preferences, and the adjustment processes are complicated in much of the literature. To overcome the defects of existing methods, we developed a novel PLPR consistency analysis model, and this paper mainly contains two sections. On the one hand, a new consistency index and the consistency checking method are proposed based on similarity measure, respectively. On the other hand, based on the idea of minimum adjustment, we constructed an optimization model to improve the consistency level and develop the process of decision making on the basis of consistency analysis. A numerical example about talent recruitment is given to verify the feasibility of the proposed method. We have a comparative analysis with Zhang’s method from many aspects including the decision results, consistency checking and improvement, as well as adjusted preferences, adjustment costs and consistence threshold. At length, the conclusion of this research is that the proposed consistency analysis model is superior to the previous method on the determination of adjustment parameter, as well as the adjustment cost and the retention of original preferences. To show the effectiveness and superiority, we have a comparative analysis with other approaches. At length, the conclusion of this study is drawn.