A decentralized feedback-based consensus model considering the consistency maintenance and readability of probabilistic linguistic preference relations for large-scale group decision-making

With the enrichment of large-scale group decision-making (LSGDM) methods, the decentralized consensus reaching process (CRP) has demonstrated many advantages. However, when the probabilistic linguistic preference relation (PLPR) is utilized in the decentralized CRP, its consistency and readability are hardly to maintain. Besides, the low-cost consensus adjustment and non-cooperative behaviors of subgroups are still not considered simultaneously in the decentralized CRP. In order to solve these problems, this article proposes a decentralized feedback-based consensus model to support CRP in LSGDM based on PLPR with complete readability. First, to maintain the consistency of PLPR throughout the LSGDM process, an additive expected consistency for PLPR is specifically defined. This definition enables the automatic consistency maintenance of PLPR during linear-weight-based clustering, opinion adjustment, and opinion aggregation. Given that the existing consistency adjustment method always destroys the readability of the original PLPR, a definition of complete readability for PLPR, reflected by a reasonable probability distribution of its elements, is proposed. This is followed by a consistency-improving optimization model that considers both the adjustment cost and complete readability. Subsequently, in order to support a more realistic CRP, a decentralized feedback-based minimum cost consensus model is established to improve the group consensus level while addressing the non-cooperative behaviors of subgroups. Furthermore, an illustrative example of the selection of expressway repair plans is presented to testify the practicality of the proposed methods and demonstrate the distinctive characteristics in comparison with the existing approaches.