Deriving priority weights from hesitant fuzzy preference relations in view of additive consistency and consensus

Given that deriving priority weights is essential in group decision making, this study focuses on deriving priority weights from hesitant fuzzy preference relation (HFPR) in view of additive consistency and consensus. To achieve this goal, first, a new additive consistency concept of the HFPR is proposed. The main feature of the proposed additive consistency concept is that it considers all evaluation information provided by decision makers, that is, neither add values into nor remove values from hesitant fuzzy elements. Second, a programming model is constructed to verify the complete additive consistency of HFPR, an additive consistency index is suggested to validate its consistency degree, and then, a programming model is established to improve its consistency degree. Third, an algorithm is designed to derive a priority weight vector from the HFPR, and the proposed algorithm not only addresses the situation in which the HFPR is a complete and acceptable additive consistency. Fourth, a programming model is presented to determine the decision makers’ weights, and then, a consensus measure index based on extraction priority weight vectors is introduced. Moreover, a programming model is constructed to derive the priority weights that correspond to expected consensus levels. Finally, the most cost-effective car selection problems are provided to illustrate the effectiveness of the proposed method. Comparative studies with several existing methods are also provided.