Consistency-based risk assessment with probabilistic linguistic preference relation - Zhang, Yixin; Xu, -->Zeshui; Wang, Hai; Liao, Huchang (Applied soft computing, 2016)
[Display omitted] •Propose the probabilistic linguistic preference relation (PLPR).•Discuss the consistency of PLPR from the perspective of digraph.•Present the consistency and acceptable consistency measures of PLPR.•Establish an optimization model to improve the consistency of PLPR.•Apply the proposed method to risk assessment. In recent years, the “Belt and Road” has aroused great attention of international society. It not only produces opportunities for China but also brings challenges: when Chinese investors invest to other countries, they will analyze the present situation of alternative countries and then assess the investment risk of these countries. Hence, how to assess the risk level of alternative countries correctly is pivotal. Moreover, affected by many factors such as decision makers (DMs)’ lacking of knowledge and the complexity of decision making problems, the DMs usually cannot use precise numbers to describe their preference information. Therefore, the use of linguistic variables is practical. As a type of linguistic term set, the probabilistic linguistic term set (PLTS) can reflect different importance degrees or weights of all possible evaluation values of a specific object. What’s more, when the DMs use linguistic variables to express their judgements, they sometimes cannot give their evaluation values for attributes directly. In such a case, the DMs usually provide their judgements by pairwise comparison of alternatives. In this paper, we introduce the concept of probabilistic linguistic preference relation (PLPR) to present the DMs’ preferences. The additive consistency of the PLPR is discussed from the perspective of the preference relation graph. Then, the consistency index of the PLPR is defined to measure the consistency. We also introduce the acceptable consistency of the PLPR. Moreover, as for the unacceptable consistent PLPR, an automatic optimization method is proposed to improve its consistency until acceptable. Once all the PLPRs are of acceptable consistency, we directly use the aggregation operators to obtain the comprehensive preference values of alternatives and then rank the alternatives according to the derived preference values. Finally, an application example involving the “Belt and Road” is given and the discussion about the results is conducted.