Analysis of acceptable additive consistency and consensus of group decision making with interval-valued hesitant fuzzy preference relations

Interval-valued hesitant fuzzy sets are efficient to denote the hesitant and uncertain judgments of decision makers. To further research the utilization of this type of fuzzy sets, this paper limits to study group decision making (GDM) with interval-valued hesitant fuzzy preference relations (IVHFPRs). First, an additive consistency index is defined for interval fuzzy preference relations, by which we derive a new acceptable additive consistency concept for IVHFPRs. Then, new models based on acceptable additive consistency are built for ascertaining unknown values, and new models for judging the acceptable additive consistency of IVHFPRs are constructed. When the consistency of IVHFPRs is unacceptable, new models based on consistency and uncertain degree are constructed for obtaining acceptable additive consistency IVHFPRs that can ensure the smallest total adjustment and the minimum number of adjusted intervals. For GDM case, a new consensus index is defined to measure the agreement degree of individual judgments. When the consensus level does not satisfy requirement, new models for reaching the additive consistency and consensus requirements are built. Furthermore, a new acceptable additive consistency- and consensus-based algorithm for GDM with incomplete and unacceptable additive consistency IVHFPRs is provided. Finally, an example is given to indicate the utilization of the new algorithm and comparison analysis is made.