Three-way decision model under a large-scale group decision-making environment with detecting and managing non-cooperative behaviors in consensus reaching process

Aiming of this paper is to introduce large-scale group decision-making (LSGDM) into three-way decisions (3WDs) with decision-theoretic rough sets (DTRSs) and propose LSGDM based 3WDs under linguistic assessments. There are two parameters involved of the 3WDs with DTRSs such as conditional probability and loss functions. Here we mainly focus on the calculation of loss function using LSGDM approach. LSGDM problem is characterized by a large number of experts, multiple clusters and a mass of evaluation data given by the experts. In some cases, experts are unwilling to revise their opinions to reach a consensus. So, the proper management of experts opinions and their non-cooperative behaviors (NCBs) is necessary to establish a consensus model. An appropriate adjustment of the credibility information is also essential. Using the clustering method, the proposed model divides the experts with similar evaluations into a subgroup. In each cluster, the experts’ opinions are then aggregate. In order to measure the level of consensus among clusters, the cluster consensus index (CCI) and group consensus index (GCI) have been developed. Then, using a tool for managing the NCBs of clusters includes two components: (1) for identifying the NCBs of clusters, NCB degree has defined using CCI and GCI; (2) for consensus improvement, implemented the weight punishment mechanism to NCBs clusters. Finally, we have designed a rule for classifying the objects into three regions, and the associated cost of each object is derived for ranking the objects in each region. An example is offered for selection of the Energy project to show the effectiveness of the proposed approach.