Consistency and consensus checking and improving methods for group decision-making with hesitant fuzzy preference relations

Decision-makers (DMs) are often hesitant about the evaluations owing to objective or subjective reasons, and determined preference relations always have various limitations on the way that DMs express their evaluations. To address this, this study investigates the group decision-making (GDM) process with hesitant fuzzy preference relations (HFPRs), and develops the methods of consistency and consensus checking and improving processes. To do this, the definitions of best consistency index (BCI) and worst consistency index (WCI) are given. On account of this, the concept of acceptable additive consistent HFPR is proposed. Moreover, the methods of consistency and consensus measurement and improvement processes are introduced for GDM with HFPRs, which can automatically obtain effective and scientific consistency and consensus results. Furthermore, a priority method for HFPRs is employed to rank the alternatives. The procedure of the GDM problem with HFPRs is introduced in detail, and an example of selecting a potential supplier for a solar company is used to demonstrate the proposed method. Comparative analyses shows that the proposed method is more powerful for dealing with the hesitant and uncertain situations and greatly expands the information description scope.