Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations

In this study, a new method is proposed to address group decision making (GDM) using incomplete reciprocal preference relations (RPRs). More specifically, the multiplicative transitivity property of RPRs is first used to estimate missing values and measure the consistency of preferences provided by experts. Following this, experts are assigned weights by combining consistency weights and trust weights. The former are derived by conducting a multiplicative consistency analysis of the opinions of each expert, whereas the latter are used to measure the degree of trust in an expert harbored by others. Experts with satisfactory consistency and large trust weights should typically be assigned large weights. The consensus level is then checked to determine whether the decision making process moves forward to the selection process. If it is negative, a hybrid method consisting of delegation and feedback mechanisms is used to improve the process of arriving at a consensus. The delegation occurs when some experts decide to leave the process, which is common in GDM involving large numbers of participants. The feedback mechanism, one of the main novelties of the proposed approach, generates different advice for experts based on their consistency and trust weights. Finally, a numerical example was studied to show the practicality and efficiency of the proposed method, and the results indicated that it can provide useful insights into the GDM process.