A rational and consensual method for group decision making with interval-valued intuitionistic multiplicative preference relations

Interval-valued intuitionistic multiplicative variables (IVIMVs) can conveniently and effectively represent the uncertain multiplicative preferred and non-preferred judgements of decision makers, this paper studies group decision making (GDM) with interval-valued intuitionistic multiplicative preference relations (IVIMPRs). To calculate the interval-valued intuitionistic multiplicative priority weight vector reasonably, a new consistency concept is introduced that satisfies robustness and upper triangular property. Following this concept, models to judge the consistency and obtain consistent IVIMPRs from inconsistent ones are constructed, respectively. To address the problem of incomplete preferences, consistency-based model to determine missing values is built. Furthermore, we study the consensus for GDM with IVIMPRs and provide a new consensus approach. When an acceptable consensus level is not achieved, an interactive and automatic adjustment method is applied to reach a better consensus level. Following discussion about consistency and consensus, an algorithm for GDM is offered that can address inconsistent and incomplete IVIMPRs. Finally, a practical problem about selecting the steel supplier is selected to show the application of the new method.