An interindividual iterative consensus model for fuzzy preference relations

Consensus reaching models are widely used to derive a representative solution in group decision-making problems. Current models present limitations regarding the achievement of the agreement and keeping enough consistency for achieving valid solutions. Therefore, this paper proposed a new consensus model based on the deviation degree of two fuzzy preference relations (FPRs), in which a novel consistency index (CI) is defined to measure whether an FPR is of acceptable consistency. Additionally, an interindividual similarity index (ISI) is devised to measure the consensus degree of two FPRs. In the proposed consensus reaching process, ISI is also used to guide the two most incompatible decision-makers (DMs) to modify their judgments. The proposed iterative consensus reaching algorithm is convergent, CI preservation. After that, a stationary vector method is adopted to determine DMs' weights for the aggregation process based on DMs' opinion transition probabilities. Finally, an illustrative example and comparative analysis is given to demonstrate the effectiveness of the proposed model.